300, 400, &c., are declinable, and have different terminations for the genders. Mille, a thousand, is indeclinable, but has a declinable plural for the series of numbers which follows. A higher unit, such as a million or billion, does not exist in Latin, and a million is therefore expressed by the form of multiplication: decies centena milia, i. e., ten times a hundred thousand, or decies alone, with the omission of centena milia, at least when sestertium (HS) is added; and in like manner, vicies, two millions; octogies, eight millions; centies, ten millions; millies, a hundred millions; bis millies, two hundred millions. Note. The genitive singular uni and the dative uno, unae, are of rare occurrence, and unclassical. (Compare, however, § 49.) The plural uni, unae, una, occurs as a numeral only in connexion with pluralia tantum, i. e., such nouns as have no singular, e. g., unae nuptiae, one wedding; una castra, one camp; unae litterae, one letter. (See Chap. XXX.) Unus is used also as a pure adjective, by dropping its signification of a numeral and taking that of "alone," or "the same," e. g., Cæs., Bell. Gall., iv., 16: uni Ubii legatos miserant, the Ubians alone had sent ambassadors; Cic., Pro Flacc., 26. Lacedaemonii septingentos jam annos unis moribus vivunt, with the same manners.. Duo and tres are naturally plurals. Nom. duo, duae, duo. Nom. tres (mas. and fem.), tria. Gen. duorum, duarum, duo- Gen. trium. rum. Dat. tribus. [tria. Dat. duobus, duabus, duobus. four months each; and the subdivision of the fundamental number in the state-division into the factors 3 x 4, of which the 4 was the basis, needs not to be insisted on. The first four numerals, therefore, would be more frequently used as adjectives than any of the others, and for this reason would have inflections, which the others, whose use would be more adverbial, might want without so much inconvenience. The same remark applies to the corresponding fact with regard to the Roman numerals. Their fundamental number was three; they had three tribes, just as the Ionians had four. Besides, the old Etruscan year, which was the basis of their civil and religious arrangements, consisted of ten months, not of twelve, and therefore the division into tetrads would not hold with them " Donaldson, New Cratylus, p. 193, seq.)—Am. Ed. Note.-Ambo, ae, o, both, is declined like duo, and has likewise two forms for the accusat., ambos and ambo, which have entirely the same meaning. In connexion with pondo (pounds) we find dua pondo, and tre pondo, for duo and tria, a barbarism noticed by the ancients themselves. (Quintil., i., 5, 15.) Duum, a second form of the genit. of duo, is the regular one in compounds; as, duumvir, but is frequently used, also, in connexion with milium. Thus, Pliny says that he had compiled his work e lectione voluminum circiter duum milium; but Cæsar and Livy likewise use this form. 4. IV. quattuor.* 5. v. quinque. 6. VI. sex. 7. VII. septem. 8. VIII. octo. 9. IX. novem. 10. x. decem. 13. XIII. tredecim, or decem et tres. 14. XIV. quattuordecim 15. xv. quindecim. 16. XVI. sedecim, or decem et sex. 17. xvii. decem et septem, or septendecim. 18. XVIII. decem et octo, or duodeviginti. 19. xIx. decem et novem, or undeviginti. 20. xx. viginti. 21. xxi. unus et viginti, or viginti unus. 22. XXII. duo et viginti, or viginti duo. 23. XXIII. tres et viginti, or viginti tres. 28. XXVIII. duodetriginta, or octo et viginti. 29. XXIX. undetriginta, or 100,000. cccɔɔɔ. centum mi novem et viginti. lia. *["We cannot find any precise information upon the time of the com. mencement of the principle of local value which prevails to a certain extent throughout the Roman system, namely, that a smaller symbol before a larger one, in numbers less than one hundred, denotes a subtraction, after it an addition. This principle does not appear in the Pho 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 () 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 (D), which is called apostrophus, with a perpendicular line preceding it (IƆ), or drawn together as D, signifies 500. In every multiplication with ten a fresh apostrophus is added, thus, I=5000, = 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, C = 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 octo 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 aç, 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. I 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. 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 xiλiás, e. g., Cic., Pro Milon., 20, quo in fundo propter insanas illas substructiones facile mille hominum versabatur valentium; Philip., vi., 5, quis L. Antonio mille nummum ferret expensum, and, very frequently, mille passuum. Livy joins mille as a collective noun (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 adjective 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. 4. quartus. 2. secundus (alter). 3. tertius. 5. quintus. 6. sextus. 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 indeclina ble. The 28th, 38th, &c., are expressed also by duodetricesimus, duodequadragesimus, and the 29th, 39th, 99th, by |