According to his account, my unfortunate Ancestor,
being afflicted with rheumatism, and in the act of being felt
by a Polygon, by one sudden start accidentally transfixed
the Great Man through the diagonal; and thereby, partly in consequence
of his long imprisonment and degradation, and partly because of
the moral shock which pervaded the whole of my Ancestor's relations,
threw back our family a degree and a half in their ascent
towards better things. The result was that in the next generation
the family brain was registered at only 58 degrees, and not till
the lapse of five generations was the lost ground recovered,
the full 60 degrees attained, and the Ascent from the Isosceles
finally achieved. And all this series of calamities from one
little accident in the process of Feeling.
At this point I think I hear some of my better educated
readers exclaim, "How could you in Flatland know anything about
angles and degrees, or minutes? We can SEE an angle, because we,
in the region of Space, can see two straight lines inclined
to one another; but you, who can see nothing but one straight line
at a time, or at all events only a number of bits of straight lines
all in one straight line -- how can you ever discern any angle,
and much less register angles of different sizes?"
I answer that though we cannot SEE angles, we can INFER them,
and this with great precision.
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