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PerspectivityYou may drag most of the elements in the interactive. This, a “Perspectivity”, is the simplest, purelyprojective comparison of linear intervals. It all happens in a single plane. 
• The red interval is to be compared with the black by way of the
orange and
green lines incident in point P, through these two intervals'
endpoints,
while ... • The orange interval is to be compared with the green by way of the red and black lines incident in point Q, through these two intervals' endpoints. If the endpoints do, in fact, “connect up”, (come
to be
incident) with P,
or with Q,
Now the Euclidean approach
to comparison is exactly the same as the Projective,
except that parallel, not
central, projection is invoked, and the comparison
is expected to be by size. Go here
to see how this is resolved through Perspective, and how parallel projection turns out to be central, after all!

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