Note 1.-The Roman signs for numbers have arisen from simple geometrical figures. The perpendicular line (I) is one; two lines crossing one another (X) make ten; half this figure (V) is five; the perpendicular line with a horizontal one at the lower end (L) is fifty, and if another horizontal line is added at the upper end (C) we have one hundred. From this sign arose the round C, which is accidentally, at the same time, the initial of centum. This C reversed (O), which is called apostrophus, with a perpendicular line preceding it (I), or drawn together as D, signi fies 500. In every multiplication with ten a fresh apostrophus is added, thus, 5000, [ɔɔɔ = 50,000. When a number is to be doubled, as many C are put before the horizontal line as there are Ɔ behind it. Thus, CID=1000, Cciɔɔ = 10,000, &c. A thousand is expressed in MSS. by , which is evidently a contraction of CIO. M, which is used for the same number, is the initial of mille.*

Note 2.-Wherever, in the above list, two numerals are put together, the first is always preferable. Forms like octodecim and novendecim, which are not mentioned in the list, are not supported by any authority; even septendecim, according to Priscian (De Sign. Num., 4), is not so good as decem et septem, although it is used by Cicero (In Verr., v., 47; De Leg. Agr., ii., 17; Philip., v., 7), and also by Tacitus (Annal., xiii., 6). Septem et decem, in Cicero (Cat., 6), and ecto et decem, in Pliny (Epist., viii., 18), are isolated peculiarities. Instead of octoginta we sometimes find octuaginta, and, corresponding with it, octuagies; but these forms cannot be recommended.

[§ 116.] The intermediate numbers are expressed in the following manner: from twenty to a hundred, either the smaller number, followed by et, precedes, or the greater one precedes without the et; e. g., quattuor et sexaginta, or sexaginta quattuor. For 18, 28, 38, 48, &c., and for 19, 29, 39, 49, etc., the expressions duodeviginti, duodetriginta, up to undecentum, are more frequent than decem et octo, or octo et viginti. In such combinations neither duo

nor un (unus) can be declined. Above 100, the greater number always precedes, either with or without et; as, mille unus, mille duo, mille trecenti, or mille et unus, mille et duo, mille et trecenti sexaginta sex. The et is never used twice, and poets, when they want another syllable, take ac, atque, or que, instead. There are, indeed, exceptions to this rule; but, being less common, they cannot be taken into consideration, and some of them are mere incorrect readings. (See my note on Cic., in Verrem, iv. 55.)

The thousands are generally expressed by the declinable substantive milia and the cardinal numbers; as, duo milia, tria milia, quattuor milia, decem milia, unum et vinician or Palmyrene notations, which otherwise much resemble the Roman in their principle of notation, though they approximate to pure vicenary scales, both adopting distinct symbols for twenty." (Penny Cyclop.. vol. xvi., p. 367.)]—Am. Ed.

[For another scheme of explanation, consult Penny Cyclop., vol xvi. p. 367.]-Am. Ed.

Į

ginti milia, quadraginta quinque milia. The distributive numerals are used more rarely; as, bina milia, quina milia, dena milia, quadragena sena milia. The objects counted are expressed by the genitive, which depends on the substantive milia; e. g., Xerxes Mardonium in Graecia reliquit cum trecentis milibus armatorum, unless a lower declined numeral is added, in which case things counted may be used in the same case with milia; e. g., habuit tria milia trecentos milites, or milites tria milia trecentos habuit; but even then the genitive may be used, e. g., habuit militum tria milia trecentos, or habuit tria milia militum et trecentos. (See the commentators on Livy, Axxix., 7.) It is only the poets that express the thousands by the indeclinable adjective mille, preceded by an adverbial numeral; as, bis mille equi, for duo milia equorum; they are, in general, fond of expressing a number by the form of multiplication; Ovid (Trist., iv., 10, 4), for example, says, milia decies novem, instead of nonaginta milia.

quo

Note. With regard to the construction of the word mille we add the following remarks. Mille is originally a substantive, which is indeclinable in the singular, but occurs only in the nom. and accus. As a substantive it governs the genitive, like the Greek xihús, e. g., Cic., Pro Milon., 20, in fundo propter insanas illas substructiones facile mille hominum versabatus valentium; Philip., vi., 5, quis L. Antonio mille nummum ferret expensum and, very frequently, mille passuum. Livy joins mille as a collective nour (see (366) to the plural of the verb, xxiii., 44; mille passuum inter urbem erant castraque: XXV., 24, jam mille armatorum ceperant partem. But mille is also an indeclinable adjective, and as such is most frequently used in all its cases, e. g., equites mille praemissi; senatus mille hominum numero constabat; da mihi basia mille; rem mille modis temptavit, &c. With this adjec tive mille, as with numerals in general, a genitivus partitivus may be used, according to 429, and thus we read in Livy, xxi., 61, cum octo milibus peditum, mille equitum, where the genitive stands for the ablative, owing to its close connexion with the word peditum; and xxiii., 46, Romanorum minus mille interfecti.

[§ 117.] THE ordinals denote the place in the series which any object holds, and answer to the question quotus? All of them are adjectives of three terminations,

us, a, um.

1. primus.

2. secundus (alter). 3. tertius.

4. quartus.

5. quintus.
6. sextus.

7. septimus. 8. octavus.

9. nonus. 10. decimus.

11. undecimus.

12. duodecimus.

13. tertius decimus. 14. quartus decimus. 15. quintus decimus. 16. sextus decimus. 17. septimus decimus.

18. octavus decimus, or duodevicesimus.

19. nonus decimus, or undevicesimus.

20. vicesimus, sometimes vigesimus.

21. unus et vicesimus, vicesimus primus.

22. alter et vicesimus, vicesimus secundus.

40. quadragesimus. 50. quinquagesimus. 60. sexagesimus. 70. septuagesimus. 80. octogesimus. 90. nonagesimus. 100. centesimus. 200. ducentesimus. 300. trecentesimus. 400. quadringentesi

mus.

500. quingentesimus 600. sexcentesimus. 700. septingentesimus. 800. octingentesimus. 900. nongentesimus. 1000. millesimus. 2000. bis millesimus. 3000. ter millesimus. 10,000. decies millesimus. 100,000. centies millesimus.

30. tricesimus, sometimes tri- 1,000,000. decies centies mil

gesimus.

lesimus.

[§ 118.] In expressing the intermediate numbers, the most common practice is to place the smaller number before the greater one with the conjunction et, or to make the greater number precede the smaller one without et ; as, quartus et vicesimus, or vicesimus quartus. But there are many instances in which the smaller number precedes without et; e. g., quintus tricesimus; and from 13 to 19 this is the ordinary method, though we also find tertius et decimus, decimus tertius, and decimus et tertius. (See Cic., de Invent., i., 53 and 54.) Instead of primus et vicesimus, &c., we find still more frequently unus et vicesimus, fem. una et vicesima, or with the elision of the vowel, unetvicesima, with the genitive unetvicesimae, as in Tacit., Annal., i., 45., and Hist., i., 67. The 22d, 32d, &c., is more frequently and better expressed by alter et oicesimus, or vicesimus et alter, than by secundus et vicesimus, &c. Now and then we meet with duoetvicesimus, duoettricesimus, in which case the word duo is indeclinable. The 28th, 38th, &c., are expressed also by duodetricesmus, duodequadragesimus, and the 29th, 39th, 99th, by

undetricesimus, undequadragesimus, undecentesimus, the words duo and unus (un) being indeclinable; and both forms are of more frequent occurrence than octavus and nonus et vicesimus, or vicesimus octavus, vicesimus nonus. There is a class of adjectives in anus which are derived from ordinal numerals, e. g., primanus, secundanus, tertianus, vicesimanus: they express the class or division to which a person belongs; in Roman writers they chiefly denote the legion of the soldiers, whence the first word in their compounds is feminine, e. g., tertiadecimani, quartadecimani, tertia et vicesimani; that is, soldiers of the thirteenth, fourteenth, twenty-third legion. In Tacitus we meet with the forms unetvicesimani and duoetvicesimani.

CHAPTER XXX.

III. DISTRIBUTIVE NUMERALS.

[§ 119.] DISTRIBUTIVE numerals denote an equal num ber distributed among several objects or at different times, and answer to the questions, "How many apiece?" and "How many each time?" (quoteni ?) They are always used in the plural. The English language having no corresponding numerals, has recourse to circumlocution.

Examples. Horat., Serm., i., 4, 86; Saepe tribus lectis videas coenare qua ternos, to dine four on each couch: Liv., xxx., 30; Scipio et Hannibal cum singulis interpretibus congressi sunt, each with an interpreter: Cic., in Verr., ii., 49; pueri senum septenumve denum annorum senatorium nomen nundinati sunt, boys of sixteen or seventeen years each purchased the title of senator. Liv., v., 30; Senatus consultum factum est, ut agri Veientani septena jugera plebi dividerentur, each plebeian received seven jugera. The passage in Cicero (ad Att., xvi., 8), Octavius veterans quingenos denarios dat, has the same meaning as (ad Fam., X., 32) Antonius denarios quingenos singulis militibus dat; that is, five hundred denarii to each soldier. When .ne distributive singuli is expressly added, the cardinal numeral is sometimes used; e. g., Cic., in Verr., ii., 55: singulis censoribus denarii trecenti ad statuam praetoris imperati sunt.

Hence the distributives are applied in multiplication (with adverbial numerals), the same number being taken several times; e. g., non didicit his bina quot essent; lunae curriculum conficitur integris quater septenis diebus: Gellius, xx., 7; Homerus pueros puellasque Niobae bis senos dicit fuisse, Euripides bis septenos, Sappho bis novenos, Bacchylides et Pindarus bis denos; quidam alii scriptores tres fuisse solos dixerunt. Poets in this case sometimes apply the cardinal numerals; e. g., Horace has, bis quinque viri, i. e., decemviri; and in prose we find decies (vicies, tricies) centum milia, although the form decies centena milia, mentioned above (§ 115), is much more common Distributives are farther used, instead of cardinals, with words which have no singular: e. g., bini codicilli, bina post Romulum spolia opima (see

94); and with those substantives the plural of which, though it has a different signification from the singular, yet retains the meaning of a sin. gular, e. g., aedes, castra, litterae, ludi (§ 96). It must, however, be observed that in this case the Romans commonly used uni instead of singuli, and trini instead of terni, since singuli and terni retain their own distributive sig nification. We therefore say, for example, bina castra uno die cepit; trinae hodie nuptiae celebrantur; quotidie quinas aut senas litteras accipio; for duo castra would mean "two castles;" duae aedes, "two temples;" and duae litterae, "two letters of the alphabet." This, however, is not the case with liberi (children), for this word has not the meaning of a singular (liberi are children, and not a child), and we accordingly say duo liberi, jus trium liberum, &c.

Bini is used for duo, to denote things which exist in pairs; as, bini boves, binae aures; and in Virgil, Aen., i., 317, bina manu crispans hastilia. No prose writer goes beyond this in the use of the distributives instead of the cardinals (except in combination with milia, see (116). Poets and Pliny the elder use these numerals in the singular in the sense of multiplicatives, e. g., Lucan, viii., 455; septeno gurgite, with a sevenfold whirl: Plin., xvii,, 3; campus fertilis centena quinquagena fruge, with one hundred and fifty fold corn. In the ordinary language they occur only in the plural, and as adjectives of three terminations, i, ae, a.

1. singuli.

14. quaterni deni.

60. sexageni.

2. bini.

15. quini deni.

70. septuageni.

80. octogeni.
90. nonageni.

18. octoni deni.

100. centeni.

5. quini. 6. seni.

7. septeni.

8. octoni.

9. noveni. 10. deni.

11 undeni.

12. duodeni.

13. terni deni.

A longer form of the hundreds, ducenteni, trecenteni, quadringenteni, &c., which is mentioned by Priscian, cannot be proved to exist. Here, too, there is some freedom in the combination of the numerals; instead of viceni quaterni, we may say quaterni et viceni, or quaterni viceni, and for 18 and 19 we have, also, the forms duodeviceni and undeviceni. The genitive of these numerals is commonly in um instead of orum; as, binum, ternum, quaternum, quinum, &c., but not singulum for singulorum.

"A thousand each time" might, according to analogy, be expressed by milleni, and then continued bis milleni, ter milleni, &c.; but this form is not in use, and instead of it we say singula milia, bina, terna, quaterna, quina milia e. g., Sueton., Octav., extr.; Legavit Augustus praetorianis militibus singula milia nummum (that is, one thousand to each), cohortibus urbanis quingenos, legionaris trecenos nummos: Livy: in singulis legionibus Romanis quina milia peditum, treceni equites erant. Milia alone is frequently used for singula milia, if its distributive meaning is indicated by some other word: o. g..