thus we have in Xenophon, Anab. v. 5, § 4: σταθμοὶ ἑκατὸν εἴκοσι δύο, παρασάγγαι ἑξακόσιοι καὶ εἴκοσι, στάδιοι μύριοι καὶ ὀκτακισχίλιοι καὶ ἑξαKOOLOL Very large numbers are frequently expressed by multiples of the substantive μvpiádes, to which the smaller amounts are added; thus we have δέκα μυριάδες, 100,000; τρισχίλια καὶ πέντε μυριάδες, 53,000; μυριάκις μύριαι μυριάδες, “ a billion.” We have also colloquial exaggerations, such as vaμμakóσio in the comedians and Athenæus, p. 671 a.

66

Obs. 3 In combining the numerical signs, which are indicated before each number, only the last of the same series bears the appropriate accent; thus we write x, 27; og', 260; awve', 1859; YTB, 53,682.

Obs. 4 Besides the cyphers given above, there is an older method of expressing numbers by the initial letters of "Ios for eis, IIévre, Aéka, Ἡεκατόν, Χίλιοι and Μύριοι. According to this method I is I, II 2, III 3, IIII 4; II is 5, III 6, ПIII 9; A is 10, AI 11, AП 15, AПIII 18, and so on; AA is 20, ▲▲▲▲ 40, and so on. In the same way H is 100, HH 200, X 1,000, XX 2,000, M 10,000. There were also abbreviated combinations of II and other letters; thus 50 was written F, F, i.e. mevtákis déka; 500 was written F or H, i.e. TeνTÁKIS ikaróv; 5,000 was written H, F, i.e. Tevтákis xíλioi, &c. Similarly they

β

expressed multiples of 10,000; thus 20,000 was M, 100,000 was M, 1,000,000 was M. It was also possible to express powers of 10,000 by repeating the letter M; thus MM was 100,000,000. In writing fractions eithery, & alone meant,, or the denominator was placed above é 26 the numerator; thus was written In the y' 49 works of the Greek mathematicians there are abundant examples of these numerical signs.

3 5

was written

με
K5

The rhapsodies of Homer, the symbols of the Heliastæ, and other conventional numbers, were indicated by the letters of the alphabet, counted a-w=1-24. For recollecting the place of a letter in the alphabet the combination ŋ, indicating the first letters of the last three hexads, furnishes a convenient memoria technica.

254

Ordinal Numbers (answering to the question "Which of the number?")

πρOTоs, first.

δεύτερος, second.

TρíTOs, third.

τέταρτος and τέτρατος, fourth.

πέμπτος, fifth.

ἕκτος, sixth.

ἕβδομος, seventh.

oydoos, eighth.

ἔνατος, ninth.

SéκaTOS, tenth.

évdékaтos, eleventh.

δωδέκατος and δυοκαιδέκατος, twelfth.

τρισκαιδέκατος and τρίτος καὶ δέκατος, thirteenth. τεσσαρακαιδέκατος and τέταρτος καὶ δέκατος, fourteenth.

EiKOσTós, twentieth.

EiKOσTÓS πρŴTOS, twenty-first.

Tρiaкоστós, thirtieth.

τεσσαρακοστός, fortieth.

πεντηκοστός, fiftieth.

ἑξηκοστός, sixtieth.

ἑβδομηκοστός, seventieth.

bydoŋkooτós, eightieth.

ἐνενηκοστός, ninetieth.

EKATоOTÓS, hundredth.

Siakoσioσтós, two-hundredth.

трiaкоσioσтós, three-hundredth.
Tεσσаракоσιοστós, four-hundredth.
Xiλoorós, thousandth.

μvρioσтós, ten-thousandth.

And so on.

Obs. 1 The ordinals are 'used idiomatically to denote broken numbers. (a) When the fraction only is expressed, we have a compound of the ordinals TpíTOS, TéTapTos, &c. with the word uóptov, "a part;" thus τρίτος, τέταρτος, μόριον, TрITημópiov, "one-third;" Terаprηuópiov, "one-fourth," &c. The adjective ἥμισυς expresses "one-half;" and for definite magnitudes we have compounds with ἡμι-, e. g. ἡμιτάλαντον, “ half a talent,” ἡμιώβολον οι ἡμιwfóliov, "half an obol." We may also express a fraction by saying Tŵv πέντε αἱ δύο μοῖραι οι τῶν πέντε μερῶν τὰ δύο, i. e. “ "two-fifths (Thucyd. I. 10'; Arist. Pol. II. 6), or тav eέ ai тpeîs μoîpai, i. e. "three-sixths." Or if the denominator exceeds the numerator by one only, we may omit the former, as ra dúo μépn, "two-thirds." (b) When a whole number is expressed as well as its fractional part, we may either use cardinal numbers, as πévτe yμutáλavтa, “two talents and a half;" or ordinals, as πέντε ἡμιτάλαντα, ßdoμov μтáλavrov, "six talents and the seventh a half talent," i. e. 64 talents; and as σðaμý is half a ŷxus, we have in Herodotus, II. 106, teμntîs oñibaμîs, "four cubits and a half." Compare the Latin sestertius, &c.

1 There is no reference in this passage to the usual and territorial divisions of the Peloponnesus, which were six and not five, but it is merely a computation of the relative extent of territory belonging to the Lacedæmonians.

Obs. 2 Móvos, "alone," "only," i. e. "one-ly," Ionic poûvos, is of the nature of an ordinal, and is connected with the first numeral in its original form μείς, μία, μέν.

Obs. 3 The ordinals are sometimes combined with cardinals, as in the phrase τῇ ὀγδόῃ καὶ ἐνάτῃ ἐπὶ δέκα, and the like.

Obs. 4 The following are epic forms of the ordinals: πρόμος, τρίτατος, τέτρατος, ἑβδόματος, ὀγδόατος, εἴνατος, by the side of which the ordinary forms also are used. We have, besides, devraтos, "the last." The Doric dialect has πρᾶτος by the side of πράν for πρώαν, and τέρτος is given by Choroboscus, Cramer. Anecd. II. p. 275, 23, as the Æolic form of τρίτος.

as

255 From the feminine of the ordinal may be formed a secondary ordinal expressing the day on which an event happened; 23 τριταῖος ἀπέθανεν, “ he died on the third day, i. e. τρίτῃ ἡμέρᾳ, πεμπταῖοι ἤλθομεν, “we came on the fifth day. Also the interrogative πоσтaîοs; “on what day?" "after how many days?"

66

256 We have also (a) multiple adjectives, aπλóos (-oûs), single," dπλóos (-oûs), “double," тρiπλóos (-oûs), “treble," &c. (for the declension see above, 205). Rarer forms are dipáσios, τριφάσιος, &c.

(b) Proportional adjectives are such as

Simλários, "twice as much,"
διπλάσιος,

τριπλάσιος,

Tρiπλáσios, "thrice as much,"

Tоanλáσios, "many times as much."

These answer to the question ποσαπλάσιος.

Obs. The difference between the adjectives in -óos and those in -άσιος is thus given by Ammonius (de dif. p. 43): διπλοῦς κατὰ μέγεθος, διπλάσιος κατ ̓ ἀριθμόν, i. e. διπλοῦς, duplex, defines the number of parts into which the whole is divided; dinλários, duplus, how many times a given number contains another in itself; thus Plato says (Charm. p. 168 c): ov yap coτí nov ädλov dinλáσiovýμíσeos, but (Cratyl. 408 c) : διπλοῦς ὁ λόγος ἀληθής τε καὶ ψευδής.

257 Numeral adverbs are such as

(a) Sixa, "in two ways,"

Tρixa, "in three ways,"
TÉTρaxa, "in four ways,"

&c.

answering to the adjectives in -Tλoûs, and

answering to the adjectives in -Tλáσios, probably formed from those in -πλoûs (above, 107). We have also more general adverbs of the same kind; as ισάκις, πολλάκις, πλεονάκις, &c.; the interrogative ποσάκις, and the correlatives τοσάκις, ὁποσάκις.

258 Numeral substantives, besides μupiás, which has been already mentioned, are such as μovás, "unity," dvás, “duality," τριάς, τετράς, πεμπάς (later πεντάς, or even πεμπτάς), ἑξάς, ἑπτάς, ὀκτάς, ἐννεάς, δεκάς, δωδεκάς, &c. ; εἰκάς, τριακάς, τεσσερακοντάς, &c. ; ἑκατοντάς, χιλιάς.

§ VI. Adverbs.

259 When some case of a declinable word-whether substantive, adjective, or pronoun-has fixed itself absolutely for the expression of certain secondary predications (see Syntax, 435), it is called an ADVERB. The prepositions, conjunctions, and interjections, which are generally regarded as distinct parts of speech, are, in regard to their origin and primitive use, neither more nor less than adverbs. Their right to a separate place in the grammar of an inflected language depends upon their syntactical functions only. The preposition is an adverb of place, specially defined by the apposition of the case of a noun; the conjunction is an adverb of manner, specially defined as the relative or antecedent in some connected sentences; the interjection is the vocative case of a noun, or some single sound, used as an exclamatory adverb.

260 We may treat of adverbs, as they are generally understood, with reference either to their meaning or to their form.

a. With regard to their meaning, adverbs are divided into (a) Adverbs of quality or manner; as kaipíws, "opportunely;" πρεπόντως, “ becomingly;” βαρβαρικώς, " barbarously;” ταυρηδόν, "like a bull;" avapavdóv, "openly;" ovoμaorí, "by name, naming

ly," nominatim; èçaípins, “suddenly;" odağ, “bitingly;" Xíav, 'excessively;" πрoîкa, “gratuitously," &c.

66

(B) Adverbs of place; as očкodev, "from home;" ’Oλvμπíaše, "to Olympia;" IIvooî, "at Delphi;" érépwσe, "in a different direction;" evdoet, "within," &c.

ἔνδοθι,

(7) Adverbs of time; as πpív, "before;" Tóre, "then;" víka, "when;" μos, "while;" réws, "so long as ;" Tóтe; "when?" &c.

261 6. With reference to their form (a), sometimes the adverb corresponds exactly to some existing case of the noun; as Dat. Koμion, "with abundance," i. e. "very much;" so also dŋμooía, “publicly;" idía, "privately;" κown, “in common;" Tε, "on foot;" σπoνòn, "zealously;" pt, "in the spring;" πεζῇ, ίφι, ἕκητι, ipi, "violently;" EKηTI, "willingly," &c.

Acc. ȧpxv or τǹv ȧpxýv, “at the beginning," i. e. “at all," "wholly," "entirely;" so also akuv, "at the point," “ hardly ;" δωρεάν oι προίκα, " gratis or in vain;” μακράν, "far;" πépav, "on the other side;" and especially neuter adjectives; as κaλóv, "beautifully;" Spaxéa, "briefly;" ȧvτíπaλov, "correspondingly" (Thucyd. 1. 3, § 4, vI. 23, § 1), &c. And sometimes to a noun with its preposition; as

πараxрnμа, "along with the business," i. e. "on the spot," "directly."

каÐάжеρ = каľ а Teр, "according to which things in particular," περ,

καθάπερ καθ ̓

i. e. "like."

ἐξαπίνης οἱ ἐξαίφνης = ἐξ ἀπινῆς (later αἰπεινῆς), ex pracipiti, a sudden."

ἐνσχερώ and ἐπισχερώ = ἐν σχερῷ, ἐπὶ σχερῷ, “ in order.”

The irregular forms vúкTwp and eμTodov are contractions for νυκτὸς ὥρᾳ and τὸ ἐν ποσὶν ὄν (cf. τὰ ἐν ποσὶ εἱλεύμενα. Herod. II. 76).

1 We should expect νύχθωρ, but it might be connected with ώρα, like φρυκτωρός. Rosen (Rig-Veda, Annot. p. v.) has compared the termination with the Vaidik vas-tar =mane. But the belongs to the crude form of vúкT-s, and if the generally-received etymology, which is given in the text, is to be rejected, we must conclude that vÚKTwp is a corruption of vúκTws, formed from the genitive (ablative) like the other adverbs

in -ws.