Gripla - 2021, Blaðsíða 95

93
before. Then find the next new digit, multiply it with both duples at once,
move the former duple [15v] towards the other duple by one place, and add
it there if an article remained there from that duple. Then multiply a new
digit with both the duples and take that number from the upper aligned to
the duple. Do this in the same way as often as needed, multiply the new
digit with all the duples, and move those always over one until you come
to the outermost place. If all of that number is used up which you wrote
at the beginning, then that number was a square. And the root of that
number is made up of the digits all together which you doubled together
with the last digit which you found. Multiply the root by itself and you
will have the same number as at first if you have worked correctly. If some
of the number remains after you extract the root, then that number was
not a square. And you add that number to that which you multiplied the
root and you will get the first number. And that number together, the root
and remainder, is the root for the larger number. If the first place of that
number which you wrote was even, then find a digit under the next figure
and multiply in the same way.
If you multiply correctly, then multiply a square number with itself
and that number which comes from this multiplication is called a cubicus,
or cubic, number. It is the same size on all sides. Moreover, the cube root
is the same as for the square number: Each number74 is the root of some
cubic number, or cubicus, but not every number is a cube.
If you want to find a cube root, note how big the number is and how
many places it has. Then find the nearest digit in the farthest of the thou-
sands place. We call places of the thousands all those which break only into
thousands. That is the fourth, the seventh, the tenth, the thirteenth, and
always jump over two places.
You shall start this work from the left. Multiply that digit which you
found with itself cubically. That is twice multiplied, first by itself and a
second time by that number which came from there. And next take from
the upper number this entire number aligned with that digit itself and next
triple the digit, skip over one place with that number, and set that number
in the third place before it if it is a digit. But if that is an article, set there
a cipher and the article in the next place. And if it is a compound number,
set the digit in the same place and the article the next. Next find a new
74 Hauksbók has tala here, which is missing in GKS 1812.
ALGORISMUS IN GKS 1812 4TO