becoming more and more oval to your view, and at last when you
have placed your eye exactly on the edge of the table
(so that you are, as it were, actually a Flatlander)
the penny will then have ceased to appear oval at all,
and will have become, so far as you can see, a straight line.
The same thing would happen if you were to treat
in the same way a Triangle, or a Square, or any other figure
cut out from pasteboard. As soon as you look at it with your eye
on the edge of the table, you will find that it ceases to appear
to you as a figure, and that it becomes in appearance a straight line.
Take for example an equilateral Triangle--who represents with us
a Tradesman of the respectable class. Figure 1 represents
the Tradesman as you would see him while you were bending over
him from above; figures 2 and 3 represent the Tradesman,
as you would see him if your eye were close to the level,
or all but on the level of the table; and if your eye were
quite on the level of the table (and that is how we see him
in Flatland) you would see nothing but a straight line.
When I was in Spaceland I heard that your sailors
have very similar experiences while they traverse
your seas and discern some distant island or coast
lying on the horizon. The far-off land may have bays,
forelands, angles in and out to any number and extent;
yet at a distance you see none of these (unless indeed
your sun shines bright upon them revealing the projections
and retirements by means of light and shade), nothing but
a grey unbroken line upon the water.
Well, that is just what we see when one of our triangular
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