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.

[Illustration]

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.

29.--_Chaucer's Puzzle._

[Illustration]

Chaucer himself accompanied the pilgrims. Being a mathematician and a man
of a thoughtful habit, the Host made fun of him, he tells us, saying,
"Thou lookes