Chaucer records the
painful fact that the harmony
of the
pilgrimage was
broken on occasions by the quarrels between the Friar and the
Sompnour.

At one stage the
latter threatened that ere they reached
Sittingbourne
he
would make the Friar's "heart for to mourn;" but the worthy Host
intervened and patched up a
temporary peace.

Unfortunately trouble broke
out again over a very curious dispute in this way.

At
one point of the journey
the road lay along two
sides of a
square
field, and some of the pilgrims persisted, in spite of trespass, in
cutting across from corner to corner, as they are seen to be doing in
the
illustration.

Now, the Friar startled the company by stating that there
was no need for the trespass, since one way was exactly the same
distance
as the other!

"On my faith, then," exclaimed the Sompnour, "thou art a
very fool!"

"Nay," replied the Friar, "if the company will but listen
with patience, I shall presently show how that thou art the fool, for
thou hast not wit enough in thy poor brain to prove that the diagonal
of
any square is less than two of the sides."

If
the reader will refer to
the diagrams that we
have given,
he will be
able to follow the Friar's argument.

If we suppose the side
of the field
to be 100 yards, then the distance along the two sides, A to B, and B
to
C, is 200 yards.

He undertook to prove that the diagonal distance
direct
from A to C is also 200 yards.

Now, if we take the diagonal path shown
in
Fig. 1, it is evident that we go the same distance, for every one of
the
eight straight portions of this path measures exactly 25
yards.

Similarly
in Fig. 2, the zigzag contains ten straight portions, each 20 yards
long:
that path is also the same length—200 yards.

No matter how
many steps we
make in our zigzag path, the result is most certainly always the
same.

Thus,
in Fig. 3 the steps are
very small, yet the distance must be 200
yards; as is also the case in Fig. 4, and would yet be if we needed a
microscope to detect the steps.

In this way, the Friar argued, we may
go
on straightening out that zigzag path until we ultimately reach a
perfectly straight line, and it therefore follows that the diagonal of
a
square is of exactly the same length as two of the sides.

Now,
in the face of it, this
must be wrong; and it
is in fact
absurdly
so, as we can at once prove by actual measurement if we have
any doubt.

Yet
the Sompnour could not for
the life of him point out the fallacy,
and
so upset the Friar's reasoning.

It was this that so exasperated him,
and
consequently, like many of us to-day when we get entangled in an
argument, he utterly lost his temper and resorted to abuse.

In
fact, if
some of the other pilgrims had not interposed the two would have
undoubtedly come to blows.

The reader will perhaps at once see the flaw
in the Friar's argument.

See answer