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**richsc** · 04-28-2003, 04:00 PM

I've was challenged by a retired US Army engineer to figure out how the Romans could do large engineering projects using their math system. I have since collected all sorts of books on ancient technologies and math, but have not found a good explanation of how Romans did math. There was a website that I unfortunately lost that had an explanation of the difference between IIII and IV for example. 
 
Any suggestions would be welcome!

Dan Diffendale · 05-04-2003, 04:46 PM

I know next to nothing on the subject... the only thing that comes to mind is a sentence in the Satyricon... "iam quattuor partes dicit," which is supposed to mean "already he can divide by four"... 
The commentary refers to Horace, Ars Poetica, 325 : "Romani pueri longis rationibus assem / discunt in partes centum diducere" 
 
and also to CIL xi. 1236 : "Attico ser. qui vixit ann. XX litteratus Graecis et Latinis librarius partes dixit CCC." 
 
Still doesn't help with how they actually *did* it, I guess.

rekirts · 05-06-2003, 07:08 PM

Hi, 
 
I figured they must have used some sort of abacus, so I looked up history of the abacus on google and found this: 
www.ee.ryerson.ca:8080/~e...bacus.html 
 
Wendy

06-16-2003, 07:47 AM

Salve, 
couple more things on the abacus if required. 
A real abacus is the flat top of a column or a tabletop. 
Making the same pattern as on the hand-abacus (4 below, 1 above) with stones one can calculate on just about any flat surface. 
Draw lines to make calculating easier with a piece of chalk (calx) and you immediatly see were the word CALculator comes from. 
The words inch and ounce come from the latin word UNCIA,which is a thumb-1/12 of a foot. 
 
Coming back to the abacus. 
You move the bottom row up one by one to get 1 thru 4 
Move the the top one down to make 5 and again with the 
lower line to make 6 thru 9. 
This makes 9/10. 10/10 is one in the next row to the left. 
The far right row (with 5 below and 1 on top) gives you 11/12 (12/12 being one again) so this line can be used in calculating with inches. 
The far right row can be used for either quarters of an inch or an entirely different system of calculating with 
Digiti -one finger or 1/16. 
So you can work with inches, and that's more than most electronic calculators can. 
 
The Romans also knew a system of calculating on their fingers.Far more complex than just one thru ten it used various positions of pinky, ringfinger and middle finger to form the numbers one thru nine and using different positions of index finger and thumb to make ten to ninety. 
So they could do numbers up to 99 on one hand and up to 9999 using both hands. 
There is a relief on this, in Germany I thought, picturing two men with an abacus and one man in the back counting on his fingers which often wrongly interpreted as two men playing a game with the third keeping score. 
 
There is of course also the simple version where the system of abacus is used with the four fingers being one to four, the thumb as five, and then the fingers again as six to nine.Ten is the pinky on the other hand, and so on up to ninety-nine. 
 
If you want a detailed explanation on how to use the Roman abacus in summation, dividing and so on look on the internet under the word SOROBAN, the Japanese word for abacus.There are sites which teach you how to do this. 
 
I hope this helps you explain to your friend that the Romans where not only capable of calculating their building projects but where also able to do it anywhere they wanted just using little stones and their fingers. 
 
Greets, 
Cordvs.

Caius Fabius · 06-16-2003, 08:10 AM

The Abacus is still in use in the markets of Ukraine, I bought a couple of used "Russian computers" to use at my Roman "store" and I may have one extra for sale, if someone wants to get really authentic. These have wooden beads, not stones and the beads are on wires, but when adding up the bill, they look cool.

**richsc** · 06-16-2003, 07:07 PM

I wish I could find this one website again: the point was that roman numerals such as IV and IIII for 4 really meant different things depending upon what end you were looking for or how you were using them.

Muzzaguchi · 07-06-2003, 11:51 PM

Hi, 
 
Anything by Dilke is okay (although I am not sure if he has how it was done stuff) and there was a book, Frontinus' Legacy, from Michigan Uni Press in 2001 which showed how Roman hydraulics calculations were performed and I think Frontinus' De Aquis has some calculations. 
 
Other than that I know a PhD in progess on Roman maths but I am not sure how close to completion it is. 
 
Cheers 
 
Muzzaguchi It is an unscrupulous intellect that does not pay Antiquity its due reverence - Erasmus of Rotterdam 
 
'Modern history, like a deaf man, answers questions no one asks' - Tolstoy War and Peace Ep. ii.1

**richsc** · 07-07-2003, 08:25 AM

Perhaps your PHD friend could donate a synopsis or some thoughts on such calculations? 
It occurs to me to ask, is the concept of zero necessary for engineering?

Muzzaguchi · 07-11-2003, 05:18 PM

I will ask next time I see him

Tarbicus · 08-27-2006, 05:42 PM

Roman maths? It's ... errmmm... simple :?

[url:qynpo020]http://en.wikipedia.org/wiki/Roman_arithmetic[/url]

Jona Lendering · 08-27-2006, 06:22 PM

Bill Thayer has put some articles online on the subject recently. Go here.

tlclark · 08-31-2006, 06:03 PM

I have a friend Roy Lewis, whose PhD is still pending last I heard (University of Pennsylvania, Architecture)

It's on the Pantheon which has some rather odd dimensions. I don't want to steal his thunder, since it isn't published but basically they cheated. They chose dimensions that made their calcuations easier by canceling out remainders and other mathematical artifacts.

Travis

Vedennius · 09-01-2006, 10:19 PM

Travis,

do you have an idea of when your friend's PhD is going to be published (and if it will be accessible with a reasonable degree of ease to someone in Europe Smile

)?

I'm interested in hearing his "Pantheon thunder", the theory seems quite intriguing. Makes you wonder if this would be applicable to other Roman engineering works as well, or whether it was a particular trick of that architect ...

tlclark · 09-04-2006, 02:05 AM

Quote:Travis,

do you have an idea of when your friend's PhD is going to be published (and if it will be accessible with a reasonable degree of ease to someone in Europe )?

I'm interested in hearing his "Pantheon thunder", the theory seems quite intriguing. Makes you wonder if this would be applicable to other Roman engineering works as well, or whether it was a particular trick of that architect ...

Not a clue.

He's been working on his as long as I've been working on mine. I haven't seen him since 2004 when I left for my research abroad.

Basically we are both family guys with lots of other distractions.

I seen early drafts of some chapters.

It's brilliant. It takes an architect to see some things some time. He's been urged for years to publish it and make some of it available, but as always, life intervenes.

Travis

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