P3D Euclid *not* on seeing 3D

[abram klooswyk <abram.klooswyk@xxxxxx>]

Dale Walsh wrote (P3D 3375  01 Jul 1999):
>Pending further investigation (...)
>(...) I am still curious about the original source of
>his [Euclids] statements on vision. (...)

I like this tenacious digging...

I have quoted recently my previous postings, both in P3d
(2995 and 2996) [see http://calcite.rocky.edu/p3d/]
and T3d (366 and 367), in which I referred to the English 
translation of Euclid's "Optics", published by 
Harry E. Burton in the Journal of the Optical Society of 
America 1945, vol.35 Nr.5, pages 357-372.

Euclid, author of "The Elements" (about 300 A.D.) also wrote 
other treatises, among which one on "Catoptrics", about 
mirrors, I don't know if it is translated in English, 
I have read a French translation (by Paul Ver Eecke, 
"Euclide, l'Optique et la Catoptrique", Paris 1959). 
Ver Eecke also discusses the history and the contents of
the Optics and Catoptrics, but it is in French...

Now for the *real* originals, which of course are in Greek!
The more or less definitive edition of all remaining works
of Euclid is an edition in Greek and Latin (left and right
pages): Euclidis OPERA OMNIA, [edited by] I.L. Heiberg et
H. Menge, Lipsiae [Latin for Leipzig, Germany] 1895.

Volume VII of this work is:
"Euclidis Optica, Opticorum Recensio Theonis, Catoptrica,
 cum scholiis antiquis", edidit I.L. Heiberg, Lipsiae 1895.
(It seems useless to read all of "The Elements" to find 
statements on vision, others have done that!)
The "binocular" theorems of Euclid are on page 40 to 55.
The famous theorem "When a sphere is seen by both eyes ..."
there reads: "Sphairos dia duo ommatoon horomenes ..."
(There are not enough Greek characters in ASCII...)

Sir David Brewster in his "The Stereoscope ..." (London 1856)
quotes from Euclids "binocular" theorems, and says that it
follows "that each eye sees different portions of the sphere,
and that it is seen by both eyes by the union of these two
dissimilar pictures." (p. 6)
The error is that seeing *more* of a *surface* with two eyes 
doesn't mean distance or depth perception.

I believe that I have shown in my postings that:
Several theorems of the "Optics" involve seeing different 
distances, but none of them mention seeing different 
distances with *two* eyes.
On the other hand, the theorems on vision with *two* eyes only
mention seeing *larger portions* of surfaces, but don't mention
distances. (Moreover, even binocular perception of *distance*
would not be the same as stereoscopic depth perception.)

So Euclid knew that two eyes see more than one, but he meant 
it in a quantitative sense: seeing more of a surface. 
Wheatstone for the first time demonstrated a qualitative binocular
effect: two eyes see depth.

Abram Klooswyk


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