However, let us examine it a
little. Ten persons were at play. For greater ease, they had adopted the
plan of each taking ten counters, and against these they had placed a
hundred francs under a candlestick, so that each counter corresponded to
ten francs. After the game the winnings were adjusted, and the players
drew from the candlestick as many ten francs as would represent the
number of counters. Seeing this, one of them, a great arithmetician
perhaps, but an indifferent reasoner, said--"Gentlemen, experience
invariably teaches me that, at the end of the game, I find myself a
gainer in proportion to the number of my counters. Have you not observed
the same with regard to yourselves? Thus, what is true of me must be
true of each of you, and _what is true of each must be true of all_. We
should, therefore, all of us gain more, at the end of the game, if we
all had more counters. Now, nothing can be easier; we have only to
distribute twice the number." This was done; but when the game was
finished, and they came to adjust the winnings, it was found that the
thousand francs under the candlestick had not been miraculously
multiplied, according to the general expectation. They had to be divided
accordingly, and the only result obtained (chimerical enough) was
this;--every one had, it is true, his double number of counters, but
every counter, instead of corresponding to _ten_ francs, only
represented _five_.
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