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Projective Comparisons, and One to One Correspondence —

The two photographs below are of the same object — a Cartesian graph, on paper.

     straight view     askance view

There is one-to-one correspondence of the features in photograph 2
with those in photograph 1

and, most importantly, with the features of the photographed object.

Thus, if line-pairs  converge in one photograph
(implying their meeting),
the corresponding pairs must converge in the other
and in the objective reality
- appearances notwithstanding.

From the foregoing, we must have that,

  • all the horizontal “parallels” converge to one place, say X,
  • and all the vertical “parallels” converge to another place, say Y.

So, either parallels meet,
or there are no parallels.

Essentially, we (and the camera) always see in Perspective, which compares our plotted ordinates (intervals) to the graph's axes
in Perspectivities, centered on X and Y
Drag the green ‘dash-dot’ lines on the graph below,
to bring these “meetings of parallels”, X and Y, into view.