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89
write in the first place any figure such as needed, for example, 8. But if
you want to write an article, then put a cipher before the figure, like this:
70. If you want to write a compound number, then set the figure64 before
the article, as here: 65.
A number is even if is made from groups of ten or if an even digit is
in the front. A number is odd if the digit in front is odd. There are four
even digits: 2, 4, 6, and 8. And the other four are odd digits: 3, 5, 7, and 9.
But one is neither [even nor odd] because it is not a number but rather the
origin of all number.65
There are seven branches of this art. The first branch is called addition,
the second subtraction, the third doubling, the fourth dividing in half, the
fifth multiplication, the sixth division, and the seventh to take a root. And
there are two branches for this: One is to take a root of a squared number
and another type is to extract a root from an octagonal number66 which
has the shape of a cube67.
From the right you should take away from, add, and divide in half.
From the left you should double, divide, multiply, and also extract both
types of root.
If you want to add one number to another, then write the larger number
above and set the smaller number even to it on the right. Then first add the
figure [14r] up to the number which is farthest out to the right. And if this
entire number is a digit, then write it in the same place. But if the number
is a compound, then write the digit in the first place and add the article to
that number which is in the next place before. But if an article results from
the addition, then write a cipher in the first place and add the article to that
number which stands next if some number is there, or, else, write it there
alone. But if there is a cipher there, then remove it and set the article down
there. Then add the other figures in the same way.
If you want to take one number away from another number, then write
the two numbers as in addition and always set the smaller number below,
otherwise even. Then you take away from the first figure the number that
stands below if it is possible and, if something is left, write that in same
64 Hauksbók has “fingr” (“digit”) here.
65 “Unity is the natural starting point of all number,” from Nicomachus, Introduction to
Arithmetic, ed. Martin Luther D’Ooge (New York: The Macmillan Company, 1926), 192.
66 Literally, “eight-cornered number” (átthyrnd tala).
67 verpill, or, in German, Würfel.
ALGORISMUS IN GKS 1812 4TO