A follow up on the exchanges in Littlemissk’s thread on “The Numbers Game”:
Does anybody know how the Romans did mathematics? The basics will do for a start: addition, subtraction, multiplication and division.
I recall hearing from my History teacher that there was a formal methodology preserved but I have never seen or heard reference to it and a quick google, whilst giving loads of hits, lead nowhere…
I am guessing it might involve a decimal abacus but am sure someone out there knows the SD…
Different ancient peoples used different methods, and an Encyclopedia of the Ancient World I happen to have handy mentions various techniques used in antiquity, but adds that little is known about the Roman way.
It says that supposedly a lot of claculations were done using prepared tables you’d take from books by famous mathematicians (which were in circulation). I guess you’d use an abacus for additions. For more complex multiplications, you could split it up into convenient parts; the encyclopedia mentions the example of 1763. You’d double the 63 four times, which gives you 1663, and you’d add 63 to it which gives you 1763. If one of the factors is rather small, you could simply add the number to itself over and over.
For square roots and stuff like that, you’d use methods of approximation. A few blessings of the decimal system were well known already, however. They knew, for example, that the knowledge of 22 = 4 also gives you 220 = 40, 2020 = 400 and so on.
There was a methodology for multiplying Roman numerals, but I never learned what it was. Old editions of World Book Encyclopedia (circa the 1950s) jad three stills from what looks like a puppet animated movie showing a Roman soldier trying to multiply Roman Numerals, and getting very frustrated as he fills the wall with M’s and C’s and D’s and X’s.
The romans did use a counting board to do arithmetic, and converted to and from the written numerals as needed: http://mathforum.org/dr.math/faq/faq.roman.html
However, you can use some simple rules to do arithmetic using roman numerals, as shown at the above site.
Thanks Nametag! I will have a good look but on the face of it that addresses addition and multiplication…
One of the questions that remains though is: SOURCES ?
It’s a methodology but do we know if it was the methodology actually used in the Roman world. To go back to the original thread; “How did the Romans do maths?”
But it might be linked through “mathforum” I’ll have a good look as I said…
My high school Latin teacher told us that for multiplication, you had to hire a professional called a “calculator”. Different shops would specialize in multiplication by different numbers, so if you needed to multiply something by 17, you would go pay some money to the guy at the XVII shop. In turn, he would check on a big table which had been compiled by tedious labor, and look up the answer you needed.
One presumes that the Romans avoided anything requiring multiplication whenever possible.
You’re sure your teacher wasn’t kidding?
Anyway, since the Romans didn’t have any copyright legislation whatsoever, I guess those tables would pretty soon have got sold on the forum for close to nothing, copied by cheap slave labor 
Btw, some "special2 numbers have been calculated pretty precisely if there was a demand for it. According to the encyclopedia, the cubic root of 100, which played an important role in determining measurements of catapults in proportion of the projectile you wanted to shoot, was determined pretty well.
You’ll note that I never made any claims on that count. All I can assure you is that our teacher really, in all truth, did tell us that. But Fr. Bede usually was pretty reliable, and it seems at least somewhat plausible.