THE CANTERBURY PUZZLES
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 S, 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
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