Campanalogia : $b or The art of ringing improved : with plain and easie rules to guide the practitioner in the ringing all kinds of changes, to which is added, great variety of new peals.Stedman, Fabian
Science
Campanalogia : $b or The art of ringing improved : with plain and easie rules to guide the practitioner in the ringing all kinds of changes, to which is added, great variety of new peals.
Stedman, Fabian
Bells; Change ringing
If we consider the multitude of different words, wherewith we express
our selves in Speech, it may be thought almost impossible that such
numbers should arise out of twenty four Letters; yet this Art of
variation will produce much more incredible effects. To give an instance
thereof, I will shew the numbers of every quantity of Letters from two
to twelve, that may be produced out of the Alphabet. The generality of
Words consisting of these quantities, (_viz._) two letters, three
letters, four, five, six, seven, eight, nine, ten, eleven, and twelve
letters. There are 10626 times four letters to be produced out of the
twenty four letters of the Alphabet, and not twice four all the same
Letters. There are likewise 42504 times five letters, 134596 times six
letters, 346104 times seven, 735471 times eight, 1307504 times nine,
1961256 times ten, 2496144 times eleven, and 2704156 times twelve. Now
each quantity being varied by the rules of this Art, will produce
incredible numbers. First the 10626 times four letters, being multiplied
by 24, which are the number of ways to vary each four letters, will
produce 255024 that is to say, four letters may be produced out of the
Alphabet to stand together after this manner (_a b c d_) two hundred
fifty five thousand and twenty four times, and not twice alike. And in
like manner, the 42504 times five Letters, being multiplied by 120,
which are the number of ways to vary each five, will produce 5100480.
The 134596 times six letters, being also multiplied by 720, will produce
96909120. The 346104, being multiplied by 5040, will produce 1744364160.
The 735471, being multiplied by 40320, will produce 29654190720. The
1307504, being multiplied by 362880, will produce 474467051520. The
1961256, being multiplied by 3628800, will produce 7117005772800. The
2496144, being multiplied by 39916800, will produce 99638080819200. And
lastly, the 2704156 time twelve letters, being multiplied by 479001600,
will produce 1295295050649600, which products being all added together,
as also 12696 which are the numbers consisting of two and three letters,
the whole will amount to 1402556105125320, wherein there are not two
alike, nor two letters of one sort in any one of them; which being
written or printed on large Paper in _folio_, allowing 5000 to a sheet,
they would take up 561022442 Reams of Paper and upwards, reckoning 500
sheets to a Ream: which Paper all the Houses in the City and Liberties
of _London_ would not contain; and in quantity doubtless infinitely
exceeds all the Books that ever were printed in the world, reckoning
only one of each Impression. And at the rate of five shillings the Ream,
the Paper would cost 140255610.5 Pounds sterling; which is above four
times as much as the yearly Rent of all the Lands and Houses in
_England_ amounts to. And all the people both young and old in the City
and Suburbs of _London_ (admitting they are five hundred thousand) could
Public-domain text, read in full here on John Shaqi.
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