In the discussion on how to compute with Roman Numerals everybody used
the subtractive writing of numbers like 4 = iv, 90 = xc, etc. This kind
of writing was very scarce in antiquity, as I learnt from Tropfke. It
became popular in the Middle Ages. Thus one should compare the list
John Conway wrote up in his letter of May 12th,
>
> namely 1 2 3 4 5 6 7 8 9
>
> become I II III IV V VI VII VIII IX in the units place,
> X XX XXX XL L LX LXX LXXX XC in the tens place,
> C CC CCC CD D DC DCC DCCC CM in the hundreds place.
>
with the list
I II III IIII V VI VII VIII VIIII in the units place,
X XX XXX XXXX L LX LXX LXXX LXXXX in the tens place,
C CC CCC CCCC D DC DCC DCCC DCCCC in the hundreds place,
M MM MMM MMMM D) D)M D)MM D)MMM D)MMMM in the thousends place.
Then one sees clearly that the Roman writing of numbers formerly used a mixed
radix representation, namely the one belonging to base 5, 2; 5, 2; 5, 2; ...
This is also seen from the few Roman abaci that still exist. These abaci also
have a line for the As which was divided into twelve ounces. So what they
implemented on the abaci was a system to the mixed radix base 6, 2; 5, 2; 5, 2;
5, 2; ...
This view of the Roman Numerals strongly supports John Conway's guess:
> .......... However, my guess is that they probably DID know it
> up to V by V, which permits an only slightly more complicated
> method, which is presumably roughly what the abacists used.
>
Unfortunately, we do not have a primer to computing from the ancients
Heinz Lueneburg