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In a recent question, I asked what the symbol was used for a thousand in Classical Latin, because I had heard somewhere that it was not 'M' which is what we are currently taught is the symbol (Short answer: it was 'CIↃ'!).

In the answer there it was hinted that there was more than one numeric system in use at the time ("accountants doing math with big numbers would have alternate systems").

All that does is bring up the new question, what exactly were those alternate systems for manipulating numbers in classical Latin?

Did they use different letters but in the same unwieldy fashion, eg 4 is represented two ways - IV or IIII? Did they use something like the Greek system? Or other methods beyond the apostrophus or vinculum methods?

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While there were variant symbols within the wider Roman numeral system — and many Romans taught by Greek preceptors may have made use of the Greek system, a notable example being Claudius Ptolemy's 2nd Century AD table of Chords — there were properly only two Roman systems for representing numbers: regular Roman numerals and finger-reckoning.

Accountants, architects and others who had to work with big numbers simply used regular mathematics (generally making use of a counting-board they called a tabula where they placed pebbles they called calculi) working on larger units of account (so for example sets of 1,000 sestertii termed sestertium [millia].

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Taking a look into ancient and modern written texts containing numbers, there are three types, law texts, commercial texts and scientific texts. Law texts always use the words for numbers, just for security on the one hand and for the readybility for the public who is not assumed to be able to decipher ciphers. Commercial texts whith hugh number of prices and values use the primitive Latin numerals, that need an abacus for verifying algebraic manipulations.

The sciences use whatever has been established in classical times, the Babylonian sexagesimal fractions in geometry, geography and astronomy, the 27 greek character system, nine for each ranges 1-9, 10-90, 100-900 and ticks for higer powers, that was already near to a decimal notation without a zero cipher as a hole and a placeholder for 'absentia'.

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    Do you have any references in support of the statement that the Romans used Babylonian or Greek number systems in contexts where Roman numerals were too clumsy? And what were the use contexts like? The word "sciences" isn't very clear to me here.
    – Joonas Ilmavirta
    Aug 10, 2023 at 22:21
  • I am a reasonable source, having teached such things a life long. Just take it for granted or open any book on history of Mathematics. Or delete it.
    – Roland F
    Aug 11, 2023 at 6:31
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    @RolandF: Did the request for a published source offend you, do you think it is unreasonable? You may very well be an expert on the topic, but how could strangers on the Internet know this?
    – Cerberus
    Aug 17, 2023 at 1:48
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Draconis already told you [edit: and apparently doesn't feel there's anything else to tell you besides what's already here]. The other systems besides |), (|), |)), ((|)), &c.

were drawing those together as single glyphs

Ⅾ, ↀ, ↁ, ↂ

and using overbars on the normal numbers to multiply by 1000.

D, Ī, V̄, X̄

The only thing he didn't mention is that sometimes they'd get creative and use sidebars too. There's a whole perfectly good Wikipedia article about all of these you can read at your leasure. Of course, the empire was a big place. There were Hebrew, Egyptian, Greek, Babylonian numerals &c. too if that's what you were asking.

Beyond that, what was much more common in antiquity was not having a separate shorthand for numbers at all. They weren't comfortable with it and just used words. The classic example is that they "had no 0" but that doesn't mean they didn't handle the concept of nonexistence. They just used actual words meaning none, not any, lacking, &c. to do the things we use the knowledge from our math classes to handle. An actual Roman wouldn't typically use numerals for huge numbers: they'd just use expressions like ten thousand/myriad, thousand thousand, &c. or make up some new ones out of spare prefixes and/or Greek.

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    Draconis said ""accountants doing math with big numbers would have alternate systems". I inferred from that that he knew that other systems existed which he had not explained. Are you saying that he -did- explain them? Which one was the 'accounting' method?
    – Mitch
    Jul 11, 2023 at 15:40
  • Would anyone downvoting like to point out what is actually wrong in the answer or could stand improvement? Mitch's second guessing Draconis's wording seems a fairly obnoxious reason on its own for a downvote, given Draconis having months to clarify if he was misunderstood.
    – lly
    Aug 12, 2023 at 10:07
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    @lly Perhaps some have felt that you don't quite address explicitly the main question (in bold in the original post). I got the impression from the comment that led to this question that there were systems other than the usual Roman numerals. To me ↂ and X̄ are symbol variants within a system, not a different system.
    – Joonas Ilmavirta
    Aug 13, 2023 at 12:32
  • @JoonasIlmavirta The question does explicitly answer the bolded question, which is why the downvotes without comment make no sense. Otherwise people are just penalizing me for OP's poor reading, when Draconis has been separately messaged and apparently doesn't feel there's anything to add to the current question. Meanwhile people feel 'the Romans used Babylonian numbers. trust me.' is more helpful?
    – lly
    Aug 16, 2023 at 4:48
  • @JoonasIlmavirta As far as 'those different systems don't count because I mean something else when I think about systems'... well, then start your own question on what you wish you could read about. Reread OP: He's specifically talking about the ways of writing numbers. As far as your answer (although it's covered by my link), the Roman used decimals for integers but duodecimals for fractions, marking them with S for half or dots for each 1/12. Nox Hor XIIIS would be 13½ hours of night. Nox Hor XIIIS⋮ or XIIIS:· would be 13¾.
    – lly
    Aug 16, 2023 at 4:59

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