Really BIG Numbers in Latin

How do you say 4, 800, 000 in Latin?

Large numbers in Latin work with numeral adverbs + units of mīllle.

• 4,800,000, octīens et quadrāgiēns centēna mīlia
• 5,900,487, noviēns et quīnquāgiēns centēna mīlia quadrigentī octōgintā septem.

Note that, because we don’t happen to possess a large number of fifth-grade math books from Rome, the most common place you’ll see numbers this large are records describing large sums of sestertia.

In these descriptions, the centēna mīlia is often omitted.

• 3,300,000 sestertia = ter et trīciēns sestertium = ter et trīciēns (centēna mīlia) sestertium = thrice and thirty times 100,000. 
• 2.7 billion sestertia = vīciēns ac septiēs mīliēns sestertium

(If anyone can explain why it’s sestertium and not sestertia, I’m all ears.)

For more on money matters, see my post on money.

https://latinforaddicts.wordpress.com/2012/05/05/roman-currency/

The Essential AG: 138a

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Numeral Adverbs

There are four central aspects to the Latin numeral:

• The cardinal: ūnus, duo, trēs, quattuor
• The ordinal: prīmus, secundus, tertius, quārtus
• The distributive: singulī, bīnī, ternī, quaternī
• The adverb: semel, bis, ter, quater

What is are numeral adverbs?

• Like English numeral adverbs, Latin numeral adverbs answer the question ‘how many times was something done?’
• How many times does Scylla engulf the strait each day? Thrice. [She does action x three times.]

[Side note: I first discovered the word ‘thrice’ while reading Homer in 6th grade. It’s probably the only moment of ‘word recognition’ that I can remember having. Does anyone else have stories about learning new words as a kid? I’d love to hear them in the comments.]
Here are the Latin adverbs (they answer quotiēns / quotiēs? How many times?).
1-10

• once, semel
• twice, bis
• thrice, ter
• four times, quater
• five times, quīnuiēns (or quīnquiēs, and sic for all numeral adverbs in -ēns)
• six times, sexiēns
• seven times, septiēns
• eight times, octiēns
• nine times, noviēns
• ten times, deciēns

11-19

• eleven times, ūndeciēns
• twelve times, duodeciēns
• thirteen times, terdeciēns
• fourteen times, quaterdeciēns
• fifteen times, quīndeciēns
• sixteen times, sēdeciēns
• seventeen times, septiēnsdeciēns
• eighteen times, duodēvīciēns
• nineteen times, ūndēvīciēns

20-99

• twenty times, vīciēns
• twenty-one times, semel vīciēns or vīcīens et semel or vīciēns semel (and sic for all numbers 21-99)
• twenty-two times, bis vīciēns
• twenty-nine times, ūndētrīciēns
• thirty times, trīciēns
• forty times, quadrāgiēns
• fifty times, quīnquāgiēns
• sixty times, sexāgiēns
• seventy times, septuāgiēns
• eighty times, octōgiēns
• ninety times, nōnāgiēns

100+

• 100 times, centiēns
• 200 times, ducentiēns
• 300 times, trecentiēns
• 400 times, quadringentiēns
• 500 times, quīngentiēns
• 600 times, sescentiēns
• 700 times, septingentiēns
• 800 times, octingentiēns
• 900 times, nōngentiēns
• 1000 times, mīliēns
• 2000 times, bis mīliēns
• 10,000 times, deciēns mīliēns

Thanksgiving

Hey All,

—
Latin for Addicts recently exceeded 100 hundred posts, and I just wanted to remind everyone how grateful I am to have readers. If there are any changes you’d like to see in the next 100 posts, feel free to leave them in the comments.

-Ryan

Fractions in Latin

This was totally new to me, but apparently they are the same as in English.

cardinal / numeral = 3 / 4 = three / fourths.
All fractions use the feminine gender nouns (as though partēs).

• 2/7 = duae septimae
• 3/11 = trēs ūndecimae
• 19/13 = ūndēvīgintī tertiae decimae
• 5/104 = quīnque centēnsimae quartae

Here’s one exception: fraction with 1 in the numerator

• 1/2 = dīmidia pars or dīmdium
• 1/3 = tertia pars
• 1/4 = quarta pars
• 1/6 = sexta pars
• 1/8 = octava pars

1/2 is altogether exceptional, but the rest of 1/x fractions all read neuter plural + pars

Ok, now here’s another exception:

When the fraction is x / x + 1, the fraction reads ordinal (agreeing with partēs) + partēs

• 2/3 = duae partēs
• 12/13 = duodecimae partēs
• 56/57 = quīnquāgēnsimae sextae partēs

But weight, there’s more! There are also a host of special nouns used to describe fractions of weight, coin value or land distribution. (A&G aren’t explicit if they can be used to measure other fractions—does anyone know?)

There are a lot of them. Sorry.

• 1/12 uncia, -ae
• 1/6 sextāns, -antis
• 1/4 quadrāns, -antis
• 1/3 triēns, -entis
• 5/12 quīncunx, -unctis
• 1/2 sēmis, -missis
• 7/12 septunx, -unctis
• 2/3 bēs or bēssis, bēssis
• 2/3 dōdrāns, -antis
• 5/6 dextāns, -antis
• 11/12 deunx, -unctis
• 12/12 as, assis

The Essential AG: 135e, 637

Ordinal Numerals

There are four central aspects to the Latin numeral:

• The cardinal: ūnus, duo, trēs, quattuor
• The ordinal: prīmus, secundus, tertius, quārtus
• The distributive: singulī, bīnī, ternī, quaternī
• The adverb: semel, bis, ter, quater

Ordinals are derived from cardinals, and operate as declining adjectives, in the manner of bonus, -a, -um

• The suffixes attached to cardinals are often very similar to superlative suffixes (e.g. ūndēvīcēnsimus, 19th)

The Ordinals 1st-10th

• 1st: prīmus, -a, -um
• 2nd: secundus, -a, -um or alter, altera, alterum (remember alterīus is the genitive for all genders)
• 3rd: tertius, -a, -um
• 4th: quārtus, -a, -um
• 5th: quīntus, -a, -um
• 6th: sextus, -a, -um
• 7th: septimus, -a, -um
• 8th: octāvus, -a, -um
• 9th: nōnus, -a, -um
• 10th: decimus, -a, -um

A few fun notes on these:

• The cardinal prīmus is an archaic superlative from prō
• The cardinal secundus is exactly what it appears to be—the future passive participle of sequor (to follow)
• The cardinal alter is a comparative form (like with the Greek -τερος)
• The cardinal nōnus is a contraction of novenus

Cardinals 11th-19th

• 11th: ūndecimus, -a, -um
• 12th: duodecimus, -a, -um
• 13th: tertius, -a, -um decimus, -a, -um or decimus et tertius or decimus tertius
• (thus, both words decline and have three double-declining variations with 14th-19th)
• 14th: quārtus decimus
• 15th: quīntus decimus
• 16th: sextus decimus
• 17th: septimus decimus
• 18th: duodēvicēnsimus, -a, -um or octāvus decimus, etc.
• 19th: ūndēvicēnsimus, -a, -um or nōnus decimus, etc.

Cardinals 20th-100th

• 20th: vīcēnsimus, -a, -um
• 21st: vīcēnsimus, -a, um prīmus, -a, -um or ūnus et vīcēnsimus 
• (thus, we have two distinct options from 11th – 19th, with (a) cardinal tens -> cardinal ones reversed or (b) ordinal ones -> cardinal tens; both terms will decline, where possible, for all cardinals 22nd-99th)
• 28th: duodētrīcēnsimus, -a, -um or the other two options
• 29th: ūndētrīcēnsimus, -a, -um
• 30th: trīcēnsimus, -a, -um
• 40th: quadrāgēnsimus, -a, -um
• 50th: quīnquāgēnsimus, -a, -um
• 60th: sexāgēnsimus, -a, -um
• 70th: septuāgensimus, -a, -um
• 80th: octōgēnsimus, -a, -um
• 90th: nōnāgēnsimus, -a, -um
• 100th: cēntēnsimus, -a, -um

A few fun notes on these:

• Again, note the distinct sets of options for the 11th-19th crowd and the 21st+ crowd: with 21st+, you get a mix of ordinals and cardinals, which can only lead to a really bad hangover…
• Whitaker’s Words suggests ūnetvīcēnsimus, -a, -um is an alternative form of 21st, though that may be Medieval only
• A few only sources suggest that the (n) in the 40th/50th/etc. is optional: quadrāgē(n)simus, -a, -um, though I should note that A&G don’t mention this

Ordinals 101st -1000th

• 101st: centēnsimus, -a, -um prīmus, -a, -um or ūnus et centēnsimus
• 113th: centēnsimus et tertius decimus or centēnsimus et decimus tertius
• (basically, we have a pattern very similar to 21st-99th, though recall that once we have three words in play, that et will only appears between the two highest denominations, so you will never see centēnsimus et decimus et tertius)
• (also, to be explicit, everything continues to decline, where possible)
• 200th: ducentēnsimus, -a, -um
• 300th: trecentēnsimus, -a, -um
• 400th: quadrigentēnsimus-, -a, -um
• 500th: quīngentēnsimus, -a, -um
• 600th: sescentēnsimus, -a, -um
• 700th: septigentēnsimus, -a, -um
• 800th: octigentēnsimus, -a, -um
• 900th: nōngentēnsimus, -a, -um
• 1000th: mīllēnsimus, -a, -um

I’ll get to the 1000+ crowd eventually, though it involves multiplicative forms, so brace yourself.

The Essential AG: 133

Cardinal Numerals, 11-100,000’s

There are four central aspects to the Latin numeral:

• The cardinal: ūnus, duo, trēs, quattuor
• The ordinal: prīmus, secundus, tertius, quārtus
• The distributive: singulī, bīnī, ternī, quaternī
• The adverb: semel, bis, ter, quater

The numerals 11-19 are indeclinable:

• note that 18 and 19 start counting back from twenty, while the others count up from ten
• French and Spanish (and other Romance languages?) also seem to freak out and shift form somewhere after 15; I’m not sure why no one thought a standardized 11-19 was a good idea

The numerals 20-100 are expressed as follows; bases of ten do not decline:

To achieve a number like 85, the Romans have two preferred methods:

• tens+ ones= (octōgintā quīnque mīlitēs)
• ones + et + tens =(quīnque et octōgintā mīlitēs)
• note that octōgintā et quīnque (a third option) is less common, but may appear
• also, note that numbers like 28 and 29 nine subtract as 18 and 19 above: duodētrīgintā, ūndētrīgintā, ūndēoctōgintā (79), etc.

The hundreds above 100 decline as adjectives like bonus, bona, bonum

Mille is an odd bird: it’s indeclinable as a singular (mīlle mīlitēs) but declines as a neuter plural (tria mīlia mīlitum)

• Note that there’s no typo here (though I am prone to typos): the singular mīlle has two l‘s; the plural mīlia/mīlium/mīlibus/mīlia/mīlibus has only one.
• He came with a thousand soldiers: cum mīlle mīlitibus vēnit.
• To express this sentence with three thousand, we decline tria mīlia and make mīles a partitive gentive
• He cam with three thousand soldiers: cum tribus mīlibus mīlitum vēnit.

To express numbers with three digits or more:

If et appears anywhere, it appears only between the two highest demoninations:

• 1776: mīlle (et) septigentī septuāgintā sex
• 2012: duo mīlia (et) duodecim

Cardinal Numerals, 1-10

There are four central aspects to the Latin numeral:

• The cardinal: ūnus, duo, trēs, quattuor
• The ordinal: prīmus, secundus, tertius, quārtus
• The distributive: singulī, bīnī, ternī, quaternī
• The adverb: semel, bis, ter, quater

From 1-10, only cardinals 1, 2, and 3 decline.

A few things to consider:

• ūnus will often mean ‘only’ (cf. sōlus) and occasionally ‘the same’ (cf. idem)
• where ūnus means ‘only,’ it may initiate a subjunctive clause of characteristic (the only man who may: ūnus cuī liceat.)
• the compound ūnus quisque = every single one
• the compound ūnus + superlative = the one most (the one most learned man, ūnus doctissiumus)
• duo may also have the plural genitive duum
• the word ambō (both, which retains the long ō of the lost Latin dual) declines like duo
• the compound ūnus + superlative = the one most (ūnus doctissiumus, the one most learned man)

Here’s a chart I found showing the descendents of the Latin cardinals:

(courtesy N.S. Gill; http://tiny.cc/eoiqmw)(For those of you who are curious, there are between 30 and 40 standing Romance languages, but we’ll get to numbers above 10 next post…)

The Essential AG: 133-4

Dative of Agent (2/2)

This post considers places where the Dative of Agent invades what would normally be constructions suitable to the Ablative of Agent.

With Passive Perfect Participles

With passive verbs, the Dative of Agent is most common with perfect passive participles, especially when these are virtually adjectival.

• It has been deliberated and established by me: mihi dēlīberātum et cōnstitūtum est.
• This has been provided for by you: tibi haec prōvīsa est.
• The lights have made me dizzy: lūcibus cālīgātus sum.

Note that, with the final expression, lūcibus may be either Dative or an Ablative of Instrument (but not an Ablative of Agent, since there is no ā/ab). In this case, assume it’s an Ablative of Instrument, which is altogether more common, especially with something inanimate like ‘lights.’

–
With Passive Verb

The Dative of Agent is not unheard of with standard passive verbs, especially with the poets.

• He is not seen by anyone: nōn cernitur ūllī.
• He was favored by the nymph: Nymphō fovēbātur.

With Videor

The construction ‘it seems to x‘ is expressed with videor, vidērī, visus + Dative of Agent.

• He seemed to me a horse with wings: mihi equis cum ālīs vidēbātur.
• It seemed otherwise to the gods: dīs aliter vīsum est.
• It seems to me that you are a slob: sordidus mihi vidēris.

With Probō

According to AG, probāre takes a Dative of Reference, but it’s so regularly attached that it seems like a Dative of Agent. I’m not sure I buy this, but here’s what they mean:

• This view was approved by both him and me: haec sententia et illī et mihi probābātur.
• This plan was not approved by the majority: hōc cōnsilium plēris nōn probābātur.

The Essential AG: 375

Dative of Agent (1/2)

My recent posts on the Ablative of Agent sent me back to my earlier work on the Gerund/Gerundive distinction, and I realize that I never fully articulated that gerundives take a Dative of Agent.

• This province is for you to defend: haec vōbis prōvincia est dēfendenda.
• I have to fight one thousand matches: mihi est mille certamina pugnandum.
• The armor you must wear is in the cabinet: arma gestanda tibi in armāriō sunt.

AG would like us to compare this construction to the dative of possession, viewing the gerundive as an ascribed duty for the dative Person:

• I have to fight one thousand matches: mihi est mille certamina pugnandum.
• My name is Commodus: mihi nomen Commodus est.

With the Second Passive Periphrastic construction (always gerundive + sum), the Ablative of Agent (ā/ab + ablative) may appear where a dative would be ambiguous.

• To whom must you submit: quibus est ā vōbis cēdendum?
• To whom should we give the books: quō ā nōbis librōs legendōs sunt?

The Essential AG: 374

My earlier work on the Gerund/Gerundive divide starts here. Flip posts at the bottom of the page to find the one you want. There are five of them on the topic.

Alternatives to the Ablative of Agent

There are two: per + accusative and operā + genitive.

• Recall that operā (sans ā/ab) is operating as an Ablative of Instrument
• These are constructions where the agent/instrument sense breaks down: with per, animate agents seems to work as instruments, and with operā, the (instrumental) labor of an agent take the place of that agent.

Agents with Per Construction

• Caesar was informed by scouts: Caesar ab explōrātōribus certiorātus est.
• Cesar was informed by scouts: Caesar per explōrātōrēs certiorātus est.

• He was trampled by charioteers: ab origīs compressus est.
• He was trampled by charioteers: per origās compressus est.

Agents with Operā Construction

• Caesar was informed by scouts: Caesar ab explōrātōribus certiorātus est.
• Caesar was informed by the work of scouts: Caesar operā explōrātōrum certiorātus est.

• The walls were cleaned by a slave: mūrī ab famulō lōtī sunt.
• The walls were cleaned by slave’s labor: mūrī operā famulī lōtī sunt.

–

While we’re at it, note the odd forth principle part of wash: lāvō, lāvāre, lāvī, lōtum.

• Really, it varies: it can also be lautum or lāvātum, depending on the author.

The Essential AG: 405b