Talk:Roman arithmetic

CPU Arithmetic
Shibboleth is apparently correct about multiplying and dividing in modern machine language (I haven't tried it much since about 1980), although I wish he had explained it a little to Mr. Hardy. The mul, div, imul, idiv, fmul and fdiv commands at x86 instruction listings are apparently intended for multiplying and dividing. Art LaPella 02:38, Sep 4, 2004 (UTC)


 * The CPU in modern computers generally is only able to directly perform these two simple operations. was deleted from the article.


 * The machine language may have the instructions, but that does not mean the CPU actually multiplied or divided as a single step. In the ALU/FPU of many CPUs, the actual multiplication is a series of shifts or additions performed by the processor.  The same holds true for division.  The orginal text did not state that CPUs lacked instructions to perform more than addition or subtraction (which was true with the Z80's instruction set).  I wish Shibboleth had taken the time to discussed it here first, rather than just making the deletion from the article.  --Denise Norris 04:31, Sep 4, 2004 (UTC)

Historical evidence
Is there any evidence that the algorithms presented here were, in fact, the ones used by ancient romans? --Mathish 01:08, 13 November 2005 (UTC)

I would also like to know if these algorithms are historical. There is an alternate method using cancellation for addition of values with subtractive notation, and multiplication can be done with a (presumably modern, albiet simple) multiplication table rather than the iterative solution presented here. --Dcorrin 16 November 2005

I found this guide to Roman Multiplication, but I don't know his sources. It seems like a much easier method of multiplying MDCCLXIII by CCXVII, and other large quantities. http://www.phy6.org/outreach/edu/roman.htm ih8evilstuff 15:52, 6 June 2006 (UTC)
 * If the Romans used it, surely they must have known why it works. Even if they didn't know the binary number system, they knew that a x b = a/2 x 2b, right? It's essentially still repeated addition, but just with a trick to do it faster.
 * While the multiplier is odd, remove one from the multiplier and add the multiplicand to the result. Use the aforementioned identity: halve the multiplier and double the multiplicand - this doesn't change the result. D.C. al fine.
 * You don't have to know binary to figure this out (it could be a nice stepping stone though, in either direction). Also note that 123 x 456 is a lot harder than 2 x 28044, the Romans must have known that too. Shinobu 12:40, 2 August 2006 (UTC)

Consider this:

The Romans used the abacus extensively, and Roman numerals efficiently record abacus results (hence 'IV'). The abacus is a very effective tool in experienced hands, and I very much doubt that any Romans would have bothered with rather cumbersome symbol-manipulation.

Trying to apply the symbol-manipulation approach to Roman numerals says more about expectations of people use to Arabic numerals, which are effective for such methods, than about Roman mathematics.

It all seems a bit of a red herring to me. Sawatts 17:39, 16 July 2007 (UTC)
 * The Story of 1 maintains that math was done with the abacus, and results were recorded in Roman numerals. Anyone know its source?  — Preceding unsigned comment added by True Pagan Warrior (talk • contribs) 18:57, 19 October 2011 (UTC)

Multiplication and division?
Someone should mention this:

To multiply using Roman numerals, say XXIX × XVII (29 × 17), convert it to:

(XX + IX) × (X + VII)

Then XX × X = CC, IX × X = XC, XX × VII = CXL, IX × VII = LXIII.

To multiply by 10, increase the "rank" by one: I --> X, V --> L, X --> C, L --> D, C --> M, and so on.

Add them up: CC + XC + CXL + LXIII = CDXCIII.

If anyone can figure out how to do division, I'd be pleased to hear from you! --121.7.203.64 (talk) 03:04, 30 May 2009 (UTC)


 * I don't know how the Europeans did arithemtic with Roman numerals, but the direct approach is messy. For example, 29 × 17 is XXIX × XVII. We calculate this by proceeding from left to right, as:

XXIX × XVII --    CCXC (X) LLVL (V) XXIX (I2) + XXIX (I1) --
 * Note that each subtotal line can be performed left-to-right. This requires a multiplication table where I×I=I, I×V=V, V×V=XXV, V×X=L, X×X=C, etc. Now combine the subtotals, separating them into digit groups that preserve their left-to-right order:

CC XC LL VL XX IX XX IX
 * Now reorder and combine groups of the same rank, replacing terms like VV and VL with their canonical equivalents:

CC XC C XXXXV XXXX VIIII VIIII CCC XCX XXX XXXX V VV IIII IIII CCC C XXXXX XX V X IIIII III CCCC L XXX V V III CCCC L XXX X III CCCC LXXXX III CD XL III CDXLIII
 * So XXIX × XVII = CDXLIII, which is 29 × 17 = 443. Yep, this is ugly. — Loadmaster (talk) 21:35, 17 September 2009 (UTC)

I thought this was very well done and I found it very interesting! Whether or not it was "unfounded" does not detract from its value. What is important is that some Romans COULD HAVE used these methods for calculating manually -- we don't know that they didn't. We DO know that the Mayan Indians did something like this with their number system (replacing five dots with a bar when adding and the bars with dots on the carry). So the Romans might have also in spite of their not having a true place value system like the Mayans. LawrenceRJ — Preceding unsigned comment added by LawrenceRJ (talk • contribs) 05:28, 18 February 2016 (UTC)

Ancient Roman Numeral System
The Roman Numeral System was used extensively on coins. It was a simple additive system and the symbols IV,  IX,  IL, IC, ID and IM were not part of it. Simply put it was I,II,III, IIII,V,VI, VII,VIII,VIIII,X then the I through VIIII was repeated through the next four Xs until the L symbol was used at XXXXVIIII. Clear and convincing evidence of the accuracy of my explanation comes from Roman Numerals on coins up to the 18th century when the use of combined symbols IV and IX came into vogue to show a single digit symbol 4 or 9. The Holy Roman Empire that lasted from roughly 650 A.D. to 1850 A.D. used these symbols correctly on their state and ecclisiastical coins and the Vatican and Papal states in Italy used them corectly too. Most of this crap has been promoted under the banner of artistic license. As time passes it gets worse as now math symbols are being interceded between the symbols too.

By the end of the Summer I plan to release essays on the original RN System, RN System Uses, RN Systems and Modern Calendar Systems,  RN Symbols Used In Error. The Impact of Using Roman Numerals (that are not part of the orignal) In Modern Practice.

If you have evidence of actual use of Roman Numerals Before 1500 when Arabic Numerals became popular in Europe I would be very interested. The adoption on Gregorian Calendar and Arabic Numerals occurred in Great Britian in MDCCLII and it's Colonies including the U. S. A.

Glen Shake —Preceding unsigned comment added by 72.181.213.4 (talk) 21:36, 13 June 2009 (UTC)

Just unfounded conjecture
I believe and the discussion at Wikipedia_talk:WikiProject_Mathematics seems to confirm that the Romans never did arithmetic in a way proposed by this article. It is a modern day fancy and not even a notable one as shown by the lack of citations. Therefore I have prodded it. Dmcq (talk) 02:20, 21 October 2011 (UTC)


 * Your argument that because Roman's used a counting table or abacus so therefore they did not do manual arithmetic is unconvincing as saying that because the modern-era had slide rules and IC-chip calculators the modern era did not do arithmetic manually. It is already noted that the article needs attention from an expert and clearly the citation list could be longer.  I believe the article can be improved and should not be deleted.--D. Norris 05:28, 21 October 2011 (UTC)  — Preceding unsigned comment added by Denorris (talk • contribs)


 * So you admit it is pure conjecture on your part that the topic exists? The first reference says nothing about arithmetic and the second says they used a counting board or abacus. So even the references that are there deny the topic exists. We already have an article on Roman abacus describing how it was used for arithmetic. Dmcq (talk) 09:24, 21 October 2011 (UTC)
 * I would guess they used a mental abacus or their fingers rather than ever computing mentally with Roman numerals. Using a mental abacus is quite common. Here http://www.uitti.net/stephen/soroban/index.shtml is a person describing their experience of using a mental soroban and the comparison with Roman numerals . You can see how unnecessary working with the numerals would be and there is no evidence of arithmetic workings with them that I know of. Dmcq (talk) 10:30, 21 October 2011 (UTC)


 * Why the attacks at me? This is an old page that has had lot of revisions.  When I created it, I based it on an old handout from college.  Much of that material was removed and new material inserted over time.  I sort of lost interest in this page until it popped up on my radar with your prodding.  If anything, in should be updated along the lines of the material you all have been discussing at http://en.wikipedia.org/wiki/Wikipedia_talk:WikiProject_Mathematics#Roman_arithmetic.  While there may not be mathematical worth, there is historical worth is presenting (with cites) that we really don't know much about Roman Arithmetic.  Feel free to update it.  I am happy to help edit.  --D. Norris 13:47, 21 October 2011 (UTC)

I have redirected the page now to Roman abacus as about the only thing I've ever seen title 'Roman arithmetic' says it would be difficult and they used an abacus or sand table. The best stuff I've found about it all is Literary evidence for Roman arithmetic with fractions which starts saying there were things thay would need other than an abacus for it doesn'tr give evidence and ends saying that the main work they've got probably was done using an abacus. There is an interesting bit about roman fractions in that though I think it is probably already all covered in the Roman numerals article. Dmcq (talk) 13:25, 21 October 2011 (UTC)


 * I disagree with redirecting the page even to Roman Abacus (another page I originally created, btw) for the above stated reasons. --D. Norris 13:47, 21 October 2011 (UTC)
 * Well in all that time noone has put a citation in and there is no evidence of a topic. I am sorry you think removing the article is an attack on you but stuff without any basis in reality should be removed from Wikipedia. Dmcq (talk) 19:06, 21 October 2011 (UTC)


 * The perceived attack was "So you admit it is pure conjecture on your part that the topic exists?" I don't object to the delete prod on your part as it brought the poor condition of the page to my attention. In fact, I don't really think that there is anything I originally wrote left in the article. Most of my original work was on basic add, subtract, multiply, divide methods using Roman numerals (I agree it is VERY difficult and not something to do for extensive calculations) which was cut from the article in 2007.  As I am not a fan of edit wars, I lost interest in the article at that point. --D. Norris 04:47, 22 October 2011 (UTC)


 * I've put a note on the talk page of Roman abacus that I redirected this there. Perhaps someone there might think there is a reason to not do that but I doubt it. Dmcq (talk) 19:34, 21 October 2011 (UTC)


 * As I have suggested, it may be better to think of this page from a historical perspective as part of an analysis of Roman science and technology rather than as a mathematics topic. Lets leave the redirect in place for the time being while I ponder a better way to address the topic. --D. Norris 04:47, 22 October 2011 (UTC)