the necessity of
this I will speedily demonstrate.

Place a penny on the middle of one of your tables in Space; and leaning
over it, look down upon it. It will appear a circle.

But now, drawing back to the edge of the table, gradually lower your
eye (thus bringing yourself more and more into the condition of the
inhabitants of Flatland), and you will find the penny 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 or other
acquaintances comes towards us in Flatland. As there is neither sun
with us, nor any light of such a kind as to make shadows, we have none
of the helps to the sight that you have in Spaceland. If our friend
comes closer to us we see his line becomes larger; if he leaves us it
becomes smaller; but still he looks like a straight line; be he a
Triangle, Square, Pentagon, Hexagon, Circle, what you will--a straight
Line he looks and nothing else.

You may perhaps ask h