I agree Bob, I think that is probably true (at least in many cases). However, they should still be able to come up with a mathematically precise analysis of a given situation using their own definitions, wouldn't you think?
I think the problem is that you have not explained what you are looking for very clearly. I think I understand.
Your quote from the Manual of photography is a elaboration of the writings of Brunelleschi citing an experiment using the Battistero in Florence as a subject. The picture below says more than any words. The subject on a ground glass screen matches the object.
With a pinhole camera we have a simple play of similar triangles or proportion. Which is what Brunelleschi was achieving.
But in photography and art we are not really interested in this simple set of relationships. We are more interested in the vanishing point of Alberti.
Or the two point perspective of Jean Pèlerin
Or three or more point perspective.
We use one or more points of perspective to create a visual effect, at what will be the normal viewing distance, that we expect our picture to be viewed from. We are of course manipulating Brunelleschi's "viewing tablet", for artistic purpose eliminating the correspondence between two similar triangles. The lens frees us form the perfect geometrical perspective of the pinhole camera
The problem becomes a simple trigonometrical problem dependent on the lens altering the angle of the rays of light exiting the lens.
But as a photographer I am interested in the concept of vanishing points which I can manipulate with my lenses to give a more or less dramatic result, for an image viewed from a normal viewing distance. We know that an image on a computer screen or in a book will be viewed from about 600-800mm. A picture in a gallery is viewed from a greater distance.
You have just repeated the same nonsense that you have said a dozen times before. You haven't explained anything in a mathematically precise way, just vague generalisations.
I asked you to describe your theory and your explanation if you don't like mine. But as usual, you just revert to criticising things that I have said (or that you think I have said). Please stick to talking about the science instead of persistently making it personal.
I get the impression that you have very little idea of what the scientific method is all about and how mathematics is used in science.
Unless you can come up with sensible answers to the questions I asked, I am not going to waste my time replying to you further.
To explain: suppose that I am near a busy highway and I would like to take a photograph that shows a lot of compression so that the cars on the highway appear to be much closer together than they are in reality. How do I work out where to put the camera to take such a photograph? How much compression can I expect?
Suppose that I also want to take a photograph in which the cars on the highway appear to be further apart than they actually are. How do I work out where to put the camera to take such a photo? How much further apart will the cars appear to be?
(According to Ansel Adams these things depend only on the camera position relative to the subjects of the photo.)
All this would seem to involve a theodolite or a Disto laser to measure distances and a calculator to do the mathematics.
Just take your camera with some lenses of differing focal lengths (maybe a good zoom) and find the picture you want by trail end error, It will be much quicker.