The morphology of classical Latin

5. Morphology of Numerals

Names of numbers

cardinals ordinals
I ūn-us, -a, um prīm-us, -a, -um
II du-o, -ae, -o secund-us, -a, -um
III tr-ēs, tr-ia terti-us, -a, -um
IV, IIII quattuor quart-us, -a, -um
V quīnque quīnt-us, -a, -um
VI sex sext-us, -a, -um
VII septem septim-us, -a, -um
VIII octō octāu-us, -a, -um
IX, VIIII nouem nōn-us, -a, -um
X decem decim-us, -a, -um
XI ūndecim ūndecim-us, -a, -um
XII duodecim duodecim-us, -a, -um
XIII trēdecim terti-us, -a, -um decim-us, -a, -um
XIV, XIIII quattuordecim quart-us decim-us, -a, -um
XV quīndecim quīnt-us decim-us, -a, -um
XVI sexdecim sext-us decim-us, -a, -um
XVII septendecim septim-us decim-us, -a, -um
XVIII duodēuigintī duodēuīcē(n)sim-us, -a, -um
XIX, XVIIII undēuigintī ūndēuīcē(n)sim-us, -a, -um
XX uigintī uīcē(n)sim-us
XXI uigintī ūnu-us
(or ūn-us et uigintī)
uīcē(n)sim-us prīm-us
(or ūn-us et uīcē(n)sim-us) -a, -um
XXII uigintī du-o
(or du-o et uigintī)
uīcē(n)sim-us secund-us
(or du-o et uīcē(n)sim-us) -a, -um)
XXX trīgintā trīcē(n)sim-us, -a, -um
XL XXXX quadrāgintā quadrāgē(n)sim-us, -a, -um
L quinquāgintā quinquāgē(n)sim-us, -a, -um
LX sexāgintā sexāgē(n)sim-us, -a, -um
LXX septuāgintā septuāgē(n)sim-us, -a, -um
LXXX octōgintā octōgē(n)sim-us, -a, -um
XC, LXXXX nōnāgintā nōnāgē(n)sim-us, -a, -um
C centum centē(n)sim-us, -a, -um
CC ducent-ī, -ae, -a ducentē(n)sim-us, -a, -um
CCC trecent-ī, -ae, -a trecentē(n)sim-us, -a, -um
CCCC quadringent-ī, -ae, -a quadringentē(n)sim-us, -a, -um
D quingent-ī, -ae, -a quingentē(n)sim-us, -a, -um
DC sescent-ī,-ae, -a sescentē(n)sim-us, -a, -um
DCC septingent-ī, -ae, -a septingentē(n)sim-us, -a, -um
DCCC octingent-īn –ae, -a octingentē(n)sim-us, -a, -um
DCCCC nōngent-ī, -ae, -a nōngentē(n)sim-us, -a, -um
CIC, M mīlle mīllē(n)sim-us, -a, -um
MM duo mīlia bis mīllē(n)sim-us, -a, -um
decem mīlia deciē(n)sim-us, -a, -um
centum mīlia deciē(n)s mīllē(n)sim-us, -a, -um̅
׀X̅׀ deciē(n)s centēna mīlia deciē(n)s centiē(n)s mīllē(n)sim-us, -a, -um

Numerals are morphemes which express in a specific and special way the number of things or beings indicated by the noun. They are either constituents of the determiner which correspond to cardinal numbers, or adjectives, which correspond to ordinal numbers.

  • 5.1. Cardinal numbers answer to question how many?, like: ūn-us “’one”, du-o “two”, etc.

The Latin system of denominations of numbers is a base ten system. Each number of the first ten has a particular name: ūn-us “one”, du-o “two”, tr-ēs “three”, quattuor “four”, quinque “five”, sex “six”, septem “seven”, octō “eight”, nouem “nine”, decem “ten”; the first nine are the “unities of the first decimal order”, and the tenth is the base of the system, and marks, by definition, a “unity of the second order”.

For the numbers from eleven to nineteen, the unities are grouped together by ten, and are named by doing a sum: undecim “one-ten“ (=1 + 10) “eleven”, duodecim “two-ten” (= 2+10) “twelve”, tredecim “three-ten” (= 3+10) “thirteen”, quattuordecim “four-ten” (= 4+10) “fourteen”, quindecim “five-ten” (= 5+10) “fifteen”, sēdecim “six-ten” (= 6+10) “sixteen”, septemdecim “seven-ten” (= 7+10) “seventeen”, octōdecim “eight-ten” (= 8+10) or duodēuigintī “two before twenty” (= 20-2) “eighteen”, nouemdecim: “nine-ten” (= 9+10) (undēuigintī) “one before twenty“ (= 20-1) “nineteen”.

The numbers from uigintī to trigintā which belong to the third ten are named by doing a sum: vigintī ūn-us (= 20+1) or ūn-us et uigintī “twenty one”, uigintī du-o (= 20+2) “twenty two”, uigintī tr-ēs (= 20+3) “twenty three”, uigintī quattuor (= 20+4) “twenty four”, uigintī quinque (= 20+5) “twenty five”, uigintī sex (= 20+6) “twenty six”, uigintī septem (= 20+7) “twenty seven”, uigintī octō (= 20+8) “twenty eight”, uigintī nouem (= 20+9) “twenty nine”, and trigintā “thirty”.

The multiples of the base, from twenty to ninety, are the tens or “unities of the second order”, and are named by doing a multiplication: in theory 20: “two-ten” (= 2×10), 30: “three-ten” (= 3×10), 40: “four-ten” (= 4×10), etc. as in English twenty (= 2×10 = 20), thirty (= 3×10 = 30), forty (= 4×10 = 40), fifty (= 5×10 = 50), sixty (= 6×10 = 60), seventy (= 7×10 = 60), eighty (= 8×10 = 80), ninety (= 9×10 = 90). In the Latin it is less visible, but it was originally the case. Because ui-ginti derives from *wi-kmₒt-ī “two tens”, *kmₒt-ī being the dual of *kmt, which represented in Indo-European *dkmt, reduced form of *dekmt. And -gintā of trī-gintā, quadrā-gintā, etc. is the neuter plural *kmtā with ā of *kmt. If the Latins didn’t know that uigintī corresponded to “two-tens”, they could imagine that tri-gintā was connected with the unity tr-ēs, tr-ia “three” and meant “thrice ten” or “three tens”, quadrāgintā with quattuor “four” and meant “four times ten”, quinquāgintā with quinque “five” and meant “five times ten”, sexāgintā with sex “six” and meant “six times ten”, septuāgintā with septem “eleven” and meant “eleven times ten”, octōgintā with octō “eight” and meant “eight times ten”, and nonāgintā with nōn-us “ninth” and meant “nine times ten”.

If the number of tens is superior or equal to ten, the unities are then grouped together by ten; and we get thus the hundreds or “unities of third order”: 100: centum < *(d)kmt-om, is a noun neuter meaning “the hundred”, and more precisely “a ten of tens” (cf. decem, and *kmt of the names of tens); 200: du-cent-ī, ae, -a (= 2×100); 300: tre-cent-ī, -ae, -a (= 3×100); 4001): quadringent-ī, -ae, -a ; 500: quingent-ī, -ae, -a; 600: sescent-ī, -ae, -a; 700: septingent-ī, -ae, -a; 800: octingent-ī, -ae, -a; 900: nongint-ī, -ae, -a. If we group the hundreds together by ten, we get the thousands or “unities of fourth order”: 1000: mille; 2000 : duo mīlia ; 3000 : tria mīlia ; 4000 : quattuor mīlia ; 5000: quinque mīlia ; 6000 : sex mīlia ; 7000 : septem mīlia ; 8000 : octō mīlia ; 9000 : nouem mīlia.

If we group the thousands together by ten, we get the “unities of fifth order”: 10.000: decem milia “ten thousand”, … , 100.000 : centum milia “a hundred thousand”, which marks the “unities of sixth order”.

Declension of cardinals.

Of the cardinals, only un-us, du-o and tr-ēs, and the hundreds above one hundred, i. e. ducent-ī, -ae, -a “two hundred”, tre-cent-ī, -ae, -a “three hundred”, … , nongint-ī, -ae, -a “nine hundred”, can be declined.

ūn-us, -a, -um is declined like adjectives of first class, except that the Genitive and Dative are the segments -ius and of the pronominal declension. ūn-us, -a, -um often has the meaning of “same” or “only”

  • cf. Plaut., Men. 1103: fratres … geminos una matre natos et patre uno uno die
    “any twins born to the same mother and the same father on the same day”;
  • Plaut., Truc. 187: te unum ex omnibus amat
    “she loves only you in the world”

and can be used in the plural in this sense, and also with the nouns denoting a single entity

  • Caes., ciu. 1,74,4: una castra iam facta ex binis
    “one camp was been made from two”.

Duo is thus declined:

Nom. du-o du-ae du-o
Gen. du-ōrum du-ābus du-ōrum
Dat. du-ōbus du-ābus du-ōbus
Abl. du-ōbus du-ābus du-ōbus
Acc. du-ōs du-ās du-o

Ambo “both” is declined like duo.

Tr-ēs is thus declined:

masc. and fem. neut.
Nom. tr-ēs tr-ia
Gen. tr-ium tr-ium
Dat. tr-ibus tr-ibus
Abl. tr-ibus tr-ibus
Acc. tr-īs (-ēs) tr-ia

In the numbers below 100, tens usually precede units, like: uigintī duo, trigintā quattuor; but if units precede tens, et is generally inserted: duo et uiginti, quatuor et triginta. But in the numbers above 100, the highest denomination generally stands first, the next second, etc. as in French: centum uigintī quinque. It is possible to insert et, but only between the two highest denominations: centum et vigintī quinque. When numerals are combined with any substantives, the following combinations are preferred: ūn-us et uigintī milit-ēs or uigintī milit-ēs (et) ūn-us “twenty one soldiers”. The hundreds, up to 1000, are adjectives of the first class; they therefore are declined like the plural of bon-us: trecent-ī, trecent-ae, trecent-a like bon-ī, bon-ae, bon-a.

Mille “a thousand” originally is a neuter noun, which is constructed with a defining genitive like (quoted by Aulu Gellius, 1,16,1):

  • Quadr., hist. 44 : ibi occiditur mille hominum
    “a thousand (of) men is killed”,
  • Plaut., Mil. 1079 : mille annorum … uiuont
    “they live thousand years”;
  • Cato, hist. 26 : est inde ferme mille passuum
    “there is from here about a mile”,

and is used in the singular like an indeclinable Determinant like:

  • Virg., Aen. 4,701 : cum mille hominibus
    “with a thousand men”,
  • or mille trahens uari-ōs colōr-ēs
    “drawing out a thousand various colors”.

In the plural, it is used like a neuter noun in -e of the third declension (type mar-e, tribunāl-e), and is thus declined: mīl-ia, mīl-ium, mīl-ibus, mīl-ibus, and mīl-ia. But, after mīl-ia, the name of the objects enumerated is always in the genitive:

  • du-o mīl-ia hominum
    “two thousand men”,
  • cum tr-ibus mīl-ibus mīlit-um
    “with three thousand soldiers”,
  • mīl-ia pass-uum tr-ia
    “three thousand paces (= three miles)”.

For million, billion, trillion, Latin has no special word, but it can express these highest numbers by multiplication of mille. So,

  • ter et triciens centēna milia sestertium : 3.300.000 sesterces
    : “three and thirty times a hundred thousand sesterces”;
  • uiciēs ac septiēs mīliēs centēna mīlia sestertium : 2.700.000.000 sesterces
    “twenty-seven thousand times a hundred thousand sesterces”.
  • 5.2 Ordinal numbers

are some adjectives most of the time derived from the cardinals: they answer the question in which order? like prīm-us “first”, secund-us “second”, etc. The ordinals (except secund-us, terti-us, octāu-us, and nōn-us) are formed with a adjectival suffix t-us or m-us: quart-us, quintus, sextus, and septim-us, decim-us, uīcēsim-us, centesim-us, mīllēsim-us, some even combining both: quartus decim-us, quint-us decim-us, sext-us decim-us, and uīcēsim-us quart-us, uīcēsim-us quintus, uīcēsim-us sext-us. The ordinal prīmus is strictly speaking a superlative (“furthest in front, foremost”) to the comparative prior (“in a more forward position”), and secundus is a participle of verb sequor, which means “following”; therefore they are not related to the cardinals un-us and du-o, they are the only one.

Ordinals and fractions

A fraction is expressed in Latin by a cardinal as numerator and an ordinal as denominator, which are in the feminine, because they are agreed with par-s, t-is (f.) “one of the portions into which a thing may be divised, a part”, expressed or understood: du-ae septim-ae part-ēs “two sevenths (2/7)”, tr-ēs octāu-ae (part-ēs) “three eighths (3/8)”. When the numerator is one, it is omitted, but pars is always expressed: terti-a par-s “one third (1/3)”

  • Caes., Gall. 1,30,10: tertiam partem agrī Sequanī occupāuisset “he took one third of the territory of the Sequani over”.

When the denominator is but one greater than numerator, only the numerator is given: du-ae part-ēs “two thirds”, tr-ēs part-ēs “three fourths” : cf.

  • Caes., Gall. 1,12,2: iam tr-ēs part-ēs copi-ārum … traduxisse, quart-am fere part-em citra flūmen … reliquam esse
    “already the three fourths of troops had gone across… about one fourth remained on this side of the river”.
  • 5.3. Distributive numerals and numeral adverbs
1. singul-ī, -ae, -a “one by one” semel “once”
2. bīn-ī, -ae, -a “two by two” bis “twice”
3. tern-ī, trin-ī “three by three” ter “thrice”
4. quatern-ī “four by four” quater “four times”
5. quīn-ī quīnquiē(n)s “five times”
6. sēn-ī sexiē(n)s
7. septēn-ī septiē(n)s
8. octōn-ī octiē(n)s
9. nouēn-ī nouiē(n)s
10. dēn-ī deciē(n)s
11. ūndēn-ī ūndeciē(n)s
12. duodēn-ī duodeciē(n)s
13. tern-ī dēn-ī terdeciē(n)s
20. uīcēn-ī uīciē(n)s
21. uīcēn-ī singul-ī semel et uiciē(n)s
30. trīcēn-ī trīciē(n)s
40. quadrāgēn-ī quadrāgiē(n)s
80. octōgēn-ī octōgiē(n)s
90. nōnāgēn-ī nōnāgiē(n)s
100. centēn-ī centiē(n)s
200. ducēn-ī ducentiē(n)s
300. trecēn-ī trecentiē(n)s
400. quadringēn-ī quadringentiē(n)s
500. quīngēn-ī quingentiē(n)s
800. octingēn-ī octingentiē(n)s
900. nōngēn-ī, nongentēn-ī nōningentiē(n)s
1.000. singul-a mīl-ia (mīllēn-ī) mīliē(n)s
10.000. dēn-a mīl-ia deciē(n)s mīliē(n)s
100.000. centēn-a mīl-ia centiē(n)s mīliē(n)s

Distributive numerals answer the question quotēn-ī “how many of each?” or “how many at a time?”, and are declined like the plural of adjectives of the first class. They are used as follows:

1) to mean “so many apiece”or “on each side”, with two distributives:

  • Caes., Gall. 2,20,3: ab … singulis … legionibus singulos legatos … discedere … uetuerat
    “he commanded each legate to stay at one’s post” (to not leave each troop);
  • Cic., leg. 2,29: plures autem deorum omnium, singuli singulorum sacerdotes … facultatem adferunt
    “a number of priests for all the gods, but allocated each separately to one god, gives the possibility …”

2) to mean the plural with some words like castr-a denoting a single entity:

  • Caes., ciu. 1,74,4: bīn-a castr-a : “two camps”
    trīn-a castr-a : “three camps”.

3) for the multiplications: bis bīn-a “twice two”, ter bīn-a “thrice two”, in ter septēn-īs diē-bus “in thrice seven days”.

Numeral adverbs answer the question quotiē(n)s “how many times? How often?”. They are used with mīlle to express the higher numbers:

ter et trīcīens (centēna mīlia) sēstertium “3.300.000 (litt. tree and thirty times a hundred thousand), three millions three hundred thousand sesterces”;

uīciēs ac septiēs mīliēs (centēna mīlia) sēstertium “2.700.000.000 (litt. twenty-seven thousand times a hundred thousand), two thousand eleven hundred millions sesterces”.

When the word sēstertium is combined with a numeral adverb, the phrase centēna mīlia is generally omitted. Thus deciēns sestertium means “1.000.000 sesterces”, i.e. deciēns centēn-a mīl-ia sestertium. And in the statement of large sums, the word sestertium also is often omitted; thus, sexagies, in:

  • Cic., Rosc. Am.2 : Bona patris … Sex. Rosci… sunt sexagiens
    “the goods of Sext. Roscius’s father are evaluated six millions sesterces”,

actually means sexagiēns centēna mīlia sēstertium. In the sums of money, a line above the number indicates thousands, and lines above and at the sides, indicate hundred thousands: thus

  • HS DC means 600 sēsterti-ī,
    HS D͞C = 600.000 sēsterti-ī or 600 sēsterti-a;
    HS │D͞C│= 60.000.000 sēsterti-ī or 60.000 sēsterti-a.

The problem of the word sēstertius It is either an adjective of the first class, which means “having a value of two and a half times the unit” (<*semis-tertius), and therefore “of low value”, or a masculine noun of the second declension, which means “sesterces”, i.e. “a coin or unity of money, equivalent to 2.5 asses (in abbreviated form II S(emis), become HS), or a quarter of denarius.

1. From one to a thousand, the form sestertius is usual: e. g. tr-ēs sēsterti-ī “three sesterces”, centum sēsterti-ī “a hundred sesterces”, mīlle sēsterti-ī/ “a thousand”.

2. Above a thousand, the usual genitive plural sestertium (rarely sesterti-ōrum) functions as an expansion of the noun in plural milia:

  • Quint. 7,6,11: sestertium nummum quinque milia legauerat
    “he bequeathed five thousand sesterces”
  • Liv. 45,15,2 : eos, qui praedium praediaue rustica pluris sestertium triginta milium haberent
    “they possessed one or several lands worth more than thirty thousand sesterces”.

3. And sēstertium, being not considered as a genitive plural any more, was analyzed as a neuter substantive meaning “a thousand sesterces”, sestertia taking the place of sestertium milia:

  • Catul. 103,1 : tria sestertia
    “3.000 sesterces”,
    decem sestertia “ten thousand sesterces”,
  • Cic., II Verr. 3,119 : sestertia dena,
    “ten thousand sesterces every time”,
  • Cic., Par., 6,49 : sescena sestertia
    “600.000 every time”,
  • CIL : sestertium nouies milies centena milia \\ “nine thousand times a hundred thousand sesterces = nine hundred millions sesterces (900.000.000)”.

But for the sums above centum mīlia, the words centena milia generally are not expressed, and sestertium, taking the place of sestertium centena milia, means therefore “a hundred thousand sesterces”:

  • Liv. 28,9,16: sestertium triciens, octoginta milia aeris
    « three millions (=30 x 100.000) sesterces and eighty thousands asses”;
  • Cic., Flac. 30 : sestertium ter et quadragiens
    “four millions three hundred (43 x 100.000) sesterces”;
  • Liv. 45,43,8 : sestertium ducentiens
    « twenty millions »;
  • Liv, 2, 37 : quadringenties sestertium
    fourty millions (=400 x 100.000) sesterces;
  • Cic., Phil. 2,45 : sestertium sexagiens
    “six millions (= 60 x 100.000) sesterces”;
  • Cic. off. 3,93 : sestertium miliens
    “a hundred millions (= 1000 x 100.000) sesterces”;
  • Liv. 45,40,1 : sestertium milliens ducenties
    “a hundred twenty millions” (=1200 x 100.000);
  • Cic. Phil. 12,12: sestertium septiens miliens
    “seven hundred millions (= 7.000 x 100.000) sesterces ».

And often the word sestertium is omitted; but the multiplying adverb makes it possible to understand that centena milia sestertium is to multiply by the said number:

  • Cic., Phil. 2,93 : Ubi est septiens miliens, quod est in tabulis, quae sunt ad Opis?
    “Where are the hundred millions (sesterces), which are on the register deposited in Opis’ temple?”
  • 5.4.Other words are related with the numerals,

especially the adjectives called multiplicatives, as: simplex, plic-is “single”, duplex, plic-is “double, twofold”, triplex, plic-is “triple, threefold”, quadruplex, plic-is “multiplied by four”, quinquiplex, plic-is “consisting of five parts, fivefold”, decuplex, plic-is, …, multiplex, plic-is “having many twists or turns, manifold”, and the derived nouns, like: duplum, -ī “a quantity twice as much”, quadruplum, -ī “a quantity four times as great or as much”, quinquiplum, -ī.

There are also any temporal adjectives, like: biennis “lasting two years”, triennis “3-year-old”, quadriennis, quinquennis, sexennis, septuennis, octennis, nouennis, decennis, or bimestris, -e “of, or lasting, two months”, trimestris “of three months”, quadrimestris, quinquemestris, sēme(n)stris “of six months’ duration”, and the derived nouns, like: biennium, -ī “a period of two years”, triennium “a period of three years”, quadriennium “a period of four years”, etc.

Retour au plan ou Aller au § 6.

1) « /Quadrīngentī, quīngentī, etc. have, like uīgintī, quinquāgintā, an obscure g instead of c” (cf. A. Ernout, Morphologie historique du latin, 1953 (Kuryłowiz, Jerzy, 1949, Le problème du classement des cas, in :Biuletyn Polskiego Towarystwa Jezykoznawczego, 9, 20-26-43), p. 109