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258 DOCUMENTS CONCERNING SWEDENBORG.
of numbers, to set his mind upon introducing a still more
useful computus into the world, instead of ten, he would
select such a perfect square, or cube number, as by con
tinual bisection, or halving, would at length terminate in
unity, and be better adapted to the sub-divisions of
measures, weights, coins, &c.
"Thus intent on a new arithmetic, the hero pitched
upon the number eight, as most fit for the purpose, since
it could not only be halved continually down to unity,
without a fraction, but contained within it the square of
two, and was itself the cube thereof, and was also appli
cable to the received denomination of several sorts of
weights and coins, rising to 16 and 32, the double and
quadruple of eight. Upon these first considerations, he
was pleased to command me to draw up an essay on an
octonary computus, which I completed in a few days,
with its application to the received divisions of coins,
measures, and weights, a disquisition on cubes and
squares, and a new and easy way of extracting roots, all
illustrated with examples.
66
His Majesty having cast his eye twice or thrice over
it, and observing, perhaps from some hints in the essay,
that the denary computus had several advantages not
always attended to, he did not at that time seem absolutely
to approve of the octonary; or, it is probable, he might
conceive, that though it seemed easy in theory, yet it
might prove difficult to introduce it to practice. Be this
as it may, he insisted on fixing upon some other that was
both a cube and a square number, referable to eight, and
divisible down to unity by bisection. This could be no
other than 64, the cube of 4, and square of 8, divisible
down to unity without a fraction.
" I immediately presumed to object, that such a num
ber would be too prolix, as it arises through a series of
entirely distinct and different numbers up to 64 , and then
again to its duplicate 4096, and on to its triplicate
262144, before the fourth step commences ; so that the
difficulty of such a computus would be incredible, not
only in addition and subtraction, but to a still higher
degree in multiplication and division. For the memory
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