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numerals

347. The numeral adjectives and corresponding adverbs are as follows:

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N. – Above 10,000:  δύο μῡριάδες 20,000, etc., μῡριάκις μύ^̄ριοι, i.e. 10,000 x 10,000.

348. Notation. – The system of alphabetic notation came into use after the second century b.c.  The first nine letters stand for units, the second nine for tens, the third nine for hundreds (27 letters). In addition to the 24 letters of the alphabet, three obsolete signs are employed: ς, a form identical with the late abbreviation for στ, in place of the lost Ϝ(3), once used for 6; Ϟ (koppa), in the same order as Lat. q, for 90; for 900, Ϡ sampi, probably for san, an old form of sigma, + pi. From 1 to 999 a stroke stands above the letter, for 1000's the same signs are used but with the stroke below the letter α' = 1, _'α = 1000).  Only the last letter in any given series has the stroke above: ρνζ' = 156, υα' = 401, _'αϠι' = 1910.  α̈ is sometimes used for 10,000; β^̈ for 20,000, etc.

a. In the classical period the following system was used according to the inscriptions:  Ι = 1, ΙΙΙΙ = 4, Γ (πέντε) = 5, ΓΙ = 6, Δ (δέκα) = 10, ΔΔ = 20, Η (ἑκατόν) = 100, ΗΗ = 200, Χ = 1000, Μ = 10,000, Γ^Δ (πεντάκις δέκα) = 50, ΓχΧ (πεντάκις χί^̄λιοι ̈ χί^̄λιοι) = 6000.

b. For the numbers from 1 to 24 the letters, used in continuous succession, are frequently used to designate the books of the Iliad (Α, Β, Γ, etc.) and of the Odyssey (α, β, γ, etc.).

349. The cardinals from 1 to 4 are declined as follows:

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a. εἷς is for ἑν-ς (cp. 245). The stem ἑν was originally σεμ (Lat. semel, simplex, singuli), weak forms of which are ἅ-παξ, ἁ-πλοῦς, from σμ-π- (35 b). μία stands for σμ-ια.

b. οὐδὲ εἷς, μηδὲ εἷς not even one unite (with change in accent) to form the compounds οὐδείς, μηδείς no one.  These words are declined like εἷς:  thus, οὐδείς, οὐδεμία, οὐδέν, οὐδενός, οὐδεμιᾶς, οὐδενός, etc., and sometimes in the plural (no men, none or nobodies) οὐδένες, οὐδένων, οὐδέσι, οὐδένας.  For emphasis the compounds may be divided, as οὐδὲ εἷς not one.  A preposition or ἄν may separate the two parts, as οὐδ' ἀπὸ μιᾶς from not a single one, οὐδ' ἂν ἑνί ne uni quidem.

c. πρῶτος (primus) means the first among more than two, πρότερος (prior) the first of two.

d. δύο may be used with the gen. and dat. pl., as δύο μνηνῶν of two months.  δυοῖν occurs rarely with plurals: παισὶν . . . δυοῖν D. 39.32.  δυεῖν for δυοῖν does not appear till about 300 b.c.

e. ἄμφω both, N. A. ἄμφω, G. D. ἀμφοῖν (Lat. ambo).  But both is more commonly ἀμφότεροι, -αι, -α.

f. For τέτταρες, -ράκοντα, etc., early Attic prose and tragedy have τέσσαρες, etc.

g. The first numeral is inflected in τρεῖς καὶ δέκα 13 τέτταρες καὶ δέκα 14 τρεισκαίδεκα and Ionic τεσσερεσκαίδεκα (very rare in Attic) are indeclinable.

350. The cardinals from 5 to 199 are indeclinable; from 200 the cardinals, and all the ordinals from first on, are declined like ἀγαθός.

a. Compound numbers above 20 are expressed by placing the smaller number first (with καί) or the larger number first (with or without καί).

b. For 21st, 31st, etc., εἷς (for πρῶτος) καὶ εἰκοστός (τριᾱκοστός) is permissible, but otherwise the cardinal is rarely thus joined with the ordinal.

c. Compounds of 10, 20, etc., with 8 and 9 are usually expressed by subtraction with the participle of δέω lack, as 18, 19, δυοῖν (ἑνὸς) δέοντες εἴκοσι.  So ναυσὶ μιᾶς δεούσαις τεττάρακοντα with 39 ships, δυοῖν δέοντα πεντήκοντα ἔτη 48 years; and with ordinals ἑνὸς δέον εἰκοστὸν ἔτος the 19th year.  The same method may be employed in other numbers than 8's or 9's: ἑπτὰ ἀποδέοντες τριᾱκόσιοι, i.e. 293.

d. An ordinal followed by ἐπὶ δέκα denotes the day of the month from the 13th to the 19th, as πέμπτῃ ἐπὶ δέκα on the 15th.

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351. With the collective words (996) ἡ ἵππος cavalry, ἡ ἀσπίς men with shields, numerals in -ιοι may appear even in the singular:  διᾱκοσίᾱ ἵππος 200 horse T. 1.62, ἀσπὶς μῡρίᾱ καὶ τετρακοσίᾱ 10,400 horse X. A. 1.7.10.

352. μύ̄ριοι, the greatest number expressed by a single word, means 10,000; μῡρίοι, countless, infinite.  In the latter sense the singular may be used, as μῡρίᾱ ἐρημίᾱ infinite solitude P. L. 677 E.

353. Fractions are expressed in several ways:  ἥμισυς 1/2, ὁ ἥμισυς τοῦ ἀριθμοῦ half the number, αἱ ἡμίσειαι τῶν νεῶν half of the ships, τὸ ἥμισυ τοῦ στρατοῦ half the army, ἡμιτάλαντον half a talent; τρία ἡμιτάλαντα 1 1/2 talents, τρίτον ἡμίμναιον 2 1/2 minae; τριτημόριον 1/3, πεμπτημόριον 1/5, ἐπίτριτος 1 1/3, ἐπίπεμπτος 1 1/5, τῶν πέντε αί δύο μοῖραι 2/5.  But when the numerator is less by one than the denominator, the genitive is omitted and only the article and μέρη are used: as τὰ τρία μέρη 3/4, i.e. the three parts (scil. of four).

354. Other classes of numeral words.

a. Distributives proper, answering the question how many each? are wanting in Greek.  Instead, ἀνά, εἰς, and κατά, with the accus., and compounds of σύν with, are used: κατὰ δύο or σύνδυο two by two, two each (Lat. bini).  The cardinals are often used alone, as ἀνδρὶ ἑκάστῳ δώσω πέντε  ἀργυρίου μνᾶς singulis militibus dabo quinas argenti minas X. A. 1.4.13 .

b. Multiplicatives in -πλοῦς -fold (from -πλοος, Lat. -plex), ἁπλοῦς simple, διπλοῦς twofold, τριπλοῦς threefold, πολλαπλοῦς manifold.

c. Proportionals in -πλασιος:  διπλάσιος twice as great or (plur.) as many, πολλαπλάσιος many times as great (many).

d. διττός means double, τριττός treble (from διχ-ιος, τριχ-ιος 112).

N. – Multiplication. – Adverbs answering the question how many times? are used in multiplication: τὰ δὶς πέντε δέκα ἐστίν twice five are ten.  See also 347 N.

e. Abstract and Collective Numbers in -άς (gen. -άδ-ος), all feminine: ἑνάς or μονάς the number one, unity, monad, δυάς the number two, duality, τριάς trinity, triad, δεκάς decad, decade, εἰκάς, ἑκατοντάς, χῑλιάς, μῡριάς myriad, ἑκατὸν μῡριάδες a million.  Also in -ύς:  τριττύς (-ύος) the third of a tribe (properly the number three), τετρακύς.

f. Adjectives in -αῖος, answering the question on what day? δευτεραῖος (or τῇ δευτεραίᾳ) ἀπῆλθε he departed on the second day.

g. Adverbs of Division. –μοναχῇ singly, in one way only, δίχα, διχῇ in two parts, doubly, τριχῇ, τέτραχα, etc., πολλαχῇ in many ways, πανταχῇ in every way.