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188 DOCUMENTS CONCERNING SWEDENBORG,
posterity. I have already touched upon the subject, in the fourth part of my
Miscellanea, treating £?e Calcido novo Sexagenario, ^c, whence M. Wolff has derived
what he has said in his Elementa Matheseos JJnnersoi, relative to this new Calcu-
lus.*
"In 1716, when M. Polheim received the king’s orders lo repair to Lund, he
engaged me to accompany him thither. Having been presented to his majesty,
he often did us the honor of conversing with us upon the different branches of
mathematics, and particularly upon mechanics, the mode of calculating forces,-
and other problems of geometry and arithmetic. He seemed to take remarkable
X^leasure in these conversations, and often put questions, as if he merely pro-
posed to gain some slight elucidation from us ; but we soon found that these
things were not strange to him, which put us, subsequently, more upon our
guard, not to speak to him of comnjon or unimportant matters, nor to advance
anything doubtful in which he might have shown us to be mistaken. The con-
versation turning upon analytical and algebraical calculation, as well as upon
what is called the regula falsi (rale of false position), he desired us to bring
forward examples, which we accordingly did, proposing such as made it in-
cumbent, in order to proceed agreeably to rule, to use signs or symbols, as weU
as equations. The king did not require them, and after a few minutes reflection,
he told us, without any other aid than his own superior genius, in what way
our examples might be solved, which we always found to agree perfectly with
our calculations. I confess, that I have never been able to understand, how, by
mere reasoning, and without the aid of Algebra, he was enabled to solve prob-
lems of this kind. It seemed, indeed, that the king was not sorry to display be-
fore M. Polheim—a competent judge in these things—a penetration and power
of reasoning, equalling those of the ablest mathematicians.
" I will now relate to you, as I am peculiarly able to do, what arose from this
learned amusement, which is as follows :
—Conversing one day with the king
upon arithmetic, and the mode of counting, we observed, that almost all nations
upon reaching 10, began again; that those figures which occupy the first place,
never change their value, while those in the second place, were multiplied ten-
fold, and so on with the others ; to which we added, that men had apparently
begun by counting their fingers, and that this method was still practised by the
people; that arithmetic having been formed into a science, figures had been in-
vented, which were of the utmost service; and, nevertheless, that the ancient
mode of counting had been always retained, in beginning again after arriving
at 10, and which is observed by putting each figure in its proper place. The
king was of opinion, that had such not been the origin of our mode of counting,
a much better and more geometrical method might have been invented, and
one which would have been of great utility in calculations, by making choice
of some other periodical number than 10. That the number 10 had this great
and necessary inconvenience, that when divided by 2, it could not be reduced
to the number 1 without entering into fractions. Besides, as it comprehends
neither the square, nor the cube, nor the fourth power of any number, many
* Christ. WolfPs Elementa Matheseos Universe, Tom. 1, p. 21, Genevae, 1743. The
passage is as follows: —" Et Carolus XII., Rex SueciaB, calculum Sexagenarium ex-
cogitavil, referente Emanuele Swedenborgio, novis characteribus efi numeris, novisque
denominationibus adinventis,"
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