Gripla - 2021, Blaðsíða 92

GRIPLA90
place, or, else, put a cipher there. But if you cannot take away the first
figure as that number which stands below is greater, then take one from
the next figure and carefully note that this makes ten [added to the figure]
in the first place. Then take from this the entire number as is below and
[write] what remains in the same place. And if ciphers stand over above,
then take one from that figure which stands next to the ciphers and write
nine where the ciphers were, all the way until you come to the place where
you want to take away from. And you will take from them ten as needed
and write what is left in the same place.
If you want to double some number, then first write such number as
you like. Next you double that figure which is farthest to the left hand and
write in the next place that which remains as in addition. But if semis68
stands over above in the outermost place, then add one since before there
was an even69 number which was divided in half.
But if you want to take half of a number, write such number as you
want and take half of the first figure if it is even. But if it was odd, then
divide in half that which remains from one less, take up the one and write
over above that character which denotes half of any part,70 which we call
semis and make so , and [if it is one, remove it and]71 put a cipher in that
place. Next take half of the second figure in the same way if it is even. But
if it is odd, then take half from that which is even and just under that and
make from this five, which is half of ten, in the place next to that. But if
one stands in the second place, then take it up and write five in next place
and put there a cipher where the one stood. A cipher does nothing unless
some figure stands to the left of it. Now proceed forward in such way for
as many figures as there are.
68 Latin for “a half-unit”; see Charlton Thomas Lewis and Charles Short, eds. Latin Dictio-
nary. (Oxford: Clarendon Press, 1969).
69 This is clearly an error, which appears as well in Hauksbók (but not in AM 685 d 4to). The
text is referring to the case in which the given number was the result of halving a previous
number, resulting in a remainder of one-half. Hence the original number must have been
odd (“óiofn”), not even (“iofn”).
70 “Take up the one” refers to the one removed from the initial odd number. In some texts of
the Indian calculus, the remainder one is written above the final digit of the result; here, a
semis is written instead.
71 This text is missing both in GKS 1812 and in Hauksbók but is needed to explain that this
instruction applies only to the case in which the first digit is a one.