Numerī Rōmānī.

Numerī

Roman numbers are additive: to make larger numbers you can combine the values of the symbols. For example, II is 2, VI is 6 and LXXVII is 77. The higher values are always to the left of the lower values, and we read the number from left to right, adding the values together as we go.

To add two numbers we combine all their symbols into a single string, order that string from highest value to lowest, and then trade the doubled-up symbols in for bigger ones. As an example, adding MMDCCXXVII (2727) and MDCCXXVIII (1728) looks like this:MMDCCXXVII
MDCCXXVIII
-------
MMMDDCCCCXXXXVVIIIII
MMMMCCCCLV = 4455Only that last step has a rule to remember: 2 D's become an M, 2 V's become an X, 5 I's become a V and 5 X's become an L.

Subtractive Combinations

When a smaller symbol stands before a larger one, you subtract it from the larger one. In practice, this was not used much because it makes numbers much harder to add up. Adding 2 numbers without subtractive combinations is much easier than adding 2 numbers with subtractive combinations. The following subtractive combinations do occur:

Romans wrote IIII and VIIII all the time. The Colosseum's numbered gates are perfect witnesses: gate 44 is carved XLIIII — subtractive for the forty, additive for the four, in one breath. Roman calendars went further and wrote XIIX for 18. Subtractive spelling became a rule centuries after Rome fell, partly because IV was more concise than IIII.

The words subtract too

Subtraction is not only a habit of the symbols; it is built into the number words themselves. Latin counts the last two numbers before a round ten downwards from it, so 18 and 19 are not “ten and eight” and “ten and nine” but two and one taken away from twenty:

The pattern holds all the way up: ūndē- is “one from” and duodē- is “two from”, glued to the number being counted down from.

Counting

You do not learn a thousand numbers. Instead, you learn a few dozen, and then you build up from there.

First we start with the numbers 1 through 20:

The first three are the only cardinals below a hundred that carry gender: ūnus and duo have a separate masculine, feminine and neuter form, while trēs has one form for masculine and feminine and another for neuter. From quattuor up to a hundred the words never change shape, no matter how the noun beside them is used. Those first three also decline for case:

Past twenty the counting goes by tens, and past a hundred by hundreds. The tens are fixed words, but the hundreds are plural adjectives that agree with what they count — that is what the -ae, -a endings below stand for.

We can then combine these numbers to make vīgintī (et) ūnus for 21, ducentī quadrāgintā septem for 247, and so on.

Ordinals

Unlike most of the cardinals, the ordinals are perfectly ordinary adjectives of the bonus type: three endings, agreeing with their noun. Only the masculine is listed below. The first two are words in their own right; the rest are built straight off the number they rank.

Abacus

The Roman hand abacus was one of the earliest portable calculating devices, used in ancient Rome. It was a simple device with grooves for pebbles ordered into columns with 2 grooves per column. Each column reprented a factor of ten, and the pebbles were moved to represent the numbers. Each column had a lower groove holding four pebbles worth one each, and a shorter upper groove holding a single pebble worth five. Actual arithmetic happened on the device. Roman numerals were never meant to be calculated with, they were meant to record what the pebbles showed. The pebbles were calculī, "little stones", and that is where calculate comes from.

As an example, the following 2 illustrations show the numbers 7 and 79 on the abacus.