es, but
it would not be very easily made, and it would not be very
pretty when it was made, and so it is seldom used or spoken of.
But octagons and hexagons are very common, for they are easily
made, and they are very regular and symmetrical in form."
The object of all this is, doubtless, to impart valuable information.
But while such slipshod writing is singularly uninteresting, it may also
be censured as inaccurate. Mr. Abbott seems to think all polygons
necessarily regular. Any child can make a heptagon at once,
notwithstanding Mr. Abbott calls it so difficult. A _regular_ heptagon,
indeed, is another matter. Then what does he mean by saying octagons and
hexagons are very regular? A regular octagon is regular, though an
octagon in general is no more regular than any other figure. But Mr.
Abbott continues:--
"If you wish to see exactly what the form of an octagon is, you
can make one in this way. First cut out a piece of paper in the
form of a square. This square will, of course, have four sides
and four corners. Now, if you cut off the four corners, you
will have four new sides, for at every place where you cut off
a corner you will have a new side. These four new sides,
together with the parts of the old sides that are left, will
make eight sides, and so you will have an octagon.
"If you wish your octagon to be regular, you must be careful
how much you cut off at each corner. If you cut off too little,
the new sides which you make will not be so long as what
remains of the old ones. If you cut off too much, they will be
longer. You had better cut off a little at first from each
corner, all around, and then compare the new sides with what
is left of the old ones. You can then cut off a little more,
and so on, until you make your octagon nearly regular.
"There are other much more exact modes of making octagons than
this, but I cannot stop to describe them here."
Must we have no more pennyworths of sense to such a monstrous quantity
of verbiage than Mr. Abbott gives us here? We would defy any man to
parody that. He could teach the penny-a-liners a trick of the trade
worth knowing. The great Chrononhotonthologos, crying,
"Go call a coach, and let a coach be called,
And let the man that calleth be the caller,
And when he calleth, let him nothing call
But 'Coach! coach! coach! Oh, for
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