According to his account, my unfortunately 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.
As 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 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 on 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 an 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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