ιβ', δώδεκα, δυώδεκα, and δυοκαίδεκα, twelve. ιγ', τρισκαίδεκα and δεκατρεῖς, thirteen. ιδ', τεσσαρεσκαίδεκα and τεσσαρακαίδεκα, fourteen. ις', ἑκκαίδεκα, sixteen. ιζ', ἑπτακαίδεκα, seventeen. ιή', ὀκτωκαίδεκα, eighteen. ιθ', ἐννεακαίδεκα, nineteen. κ', εἴκοσι(ν), twenty. κα', εἷς καὶ εἴκοσι", twenty-one. 1 Instead of " eighteen” or “ nineteen,” the Greeks frequently said “twenty wanting two" or one: " e. g. νῆες δυείν or μιᾶς δέουσαι εἴκοσι, twenty ships wanting two or one, i. e. 18 or 19 ships; and so for 28, 29, 38; and this applies to detailed numbers, as in Thucyd. VII. 31: τετρακόσιοι καὶ δυοῖν δέοντες πεντήκοντα ἄνδρες, “ four hundred and forty-eight men ;" and to hundreds as well as to tens; thus we have in Thucyd. II. 31: τριακοσίων ἀποδέοντα μύρια, " nine thousand seven hundred.” 2 In the composition of two numbers, if the smaller precedes, the two are joined by καί ; if the greater, the conjunction is omitted: as πέντε καὶ εἴκοσι, Herod. ; elkort πέντε, Demosth. In Pindar, Οl. I. 128, we have the two numbers combined by τε καί. frequently used as adjectives than the others, and for this reason would have inflexions, which the others, whose use would be more adverbial, might omit without so much inconvenience. The same remark applies to the corresponding fact in regard to the numerals of the Romans, whose fundamental number was three. 247 Numerals are divided into two classes: A. Cardinals, B. Ordinals. The former express a definite number. The latter express the position of the objects in a succession of numbers. So that although the cardinal is by its origin a positional word, it includes in its meaning all the positions up to that which it designates for this is the process in counting. 248 All ordinals are declined like adjectives of three genders. 249 Α. Cardinal Numbers (answering to the question “How ιβ', δώδεκα, δυώδεκα, and δυοκαίδεκα, twelve. ιγ', τρισκαίδεκα and δεκατρεῖς, thirteen. ιδ', τεσσαρεσκαίδεκα and τεσσαρακαίδεκα, fourteen. ις', εκκαίδεκα, sixteen. ιζ', ἑπτακαίδεκα, seventeen. ιη', ὀκτωκαίδεκα, eighteen. ιθ', ἐννεακαίδεκα, nineteen. κα', εἷς καὶ εἴκοσι, twenty-one. 1 Instead of " eighteen” or “ nineteen,” the Greeks frequently said " twenty wanting two” or “one:” e. g. νῆες δυεῖν οι μιᾶς δέουσαι εἴκοσι, twenty ships wanting two or one, i. e. 18 or 19 ships; and so for 28, 29, 38; and this applies to detailed numbers, as in Thucyd. VII. 31: τετρακόσιοι καὶ δυοῖν δέοντες πεντήκοντα άνδρες, “ four hundred and forty-eight men;” and to hundreds as well as to tens; thus we have in Thucyd. II. 31: τριακοσίων ἀποδέοντα μύρια, “ nine thousand seven hundred.” 2 In the composition of two numbers, if the smaller precedes, the two are joined by καί ; if the greater, the conjunction is omitted: as πέντε καὶ εἴκοσι, Herod. ; εἴκοσι πέντε, Demosth. In Pindar, Οl. I. 128, we have the two numbers combined by τε καί. κβ', δύο καὶ εἴκοσι, twenty-two. λ', τριάκοντα, thirty, Ionic τριήκοντα. μ', τεσσαράκοντα, forty, Ionie τεσσαρήκοντα. ξ', ἑξήκοντα, sixty. ό, ἑβδομήκοντα, seventy. τ', ὀγδοήκοντα, eighty, Ionic ὀγδώκοντα. 2, 4, or 4, ἐνενήκοντα, ninety. ρ', ἑκατόν, a hundred. α σ', διακόσιοι, two hundred, Ionic διηκόσιοι, declined thus: τ', τριακόσιοι, three hundred. λ, ἐνακόσιοι (ἐννακόσιοι), nine hundred. α, χίλιοι, a thousand lit. " as in a heap of fodder"). β, δισχίλιοι, two thousand. γ, τρισχίλιοι, three thousand. In the Odyss. XVI. 249, we ought perhaps to read πίσυρες καὶ Γείκοσι for πίσυρές τε καὶ είκοσι. The cardinal numbers compounded with σύν signify: 2 “ At a time,” or the distribution of a whole number into equal aliquot parts, σύντρεις, three at a time. The same meaning may be expressed by ává and eis, the latter being used of the array of soldiers, as εἰς ὀκτώ, " eight deep." δ, τεσσαρακισχίλιοι, four thousand. P, pipio, ten thousand (lit. “as in drops of water”). Obs. 1 The following are the alterations observable in the cardinal numbers: (a) In Homer we find ἴα, τῆς for μία, μιής, and even iῷ once for ἑνί (Il. vi. 422). The forms uín, ovdeμíny are hyper-Ionic, and are found only in Hippocrates. (b) Homer and the later epic poets write Sotós, doin, dolóv, in addition to δύω and δύο. In Herodotus we find δυῶν, δυοῖσι; in Doric δυῶν, and in Aolic, according to Eustathius, δύεσιν (δύεσσιν). (c) In old Doric inscriptions we have τρις for τρεῖς ; and τριοῖσι for rpuri is quoted from Hipponax. (d) For Téoσapes, which is the form adopted by the old Ionic, by Thucydides, and the tragedians, we have TérTapes in newer Attic, réσσepes in Herodotus, rérepes in Doric and in Hesiod, Op. et D. 698, and πίσυρες οι πέσσυρες in olic. (e) The Holic form of πέντε was πέμπε, from which come the Homeric and Attic derivatives πεμπάς, πεμπάζω, &c., and the common ordinal TéμTTOS. K. O. Müller has proposed to write Téμrov for the gen. pl. in an admirable emendation of Alcæus, ap. Strab. p. 617. πέμπτος. (f) Homer writes Fείκοσι and εείκοσι. The Doric forms are εἴκατι, FIKATI, FEIKATI, Beíkari (Ahrens, Dor. Dial. p. 279), and the initial letter is retained in the Latin viginti. (g) It will be observed that the formative a in Tptákovтa, &c. is always long after a vowel, but otherwise short or changed into ŋ. In epic and Ionic Greek we have τριήκοντα and even τριηκόντων (Hesiod, Op. et D. 694). For τεσσαράκοντα the Doric dialect gives τετρώκοντα (Ahrens, Dor. Diál. p. 280). (h) As far as can be determined from the variations of the MSS., it is best to write ἐνενήκοντα and ἐνακόσιοι with a single v. (i) For χίλιοι the Lesbians wrote χέλλιοι, the Boeotians χείλιοι, and the Doric xo (Ahrens, Dor. Dial. p. 281). (j) It was customary to distinguish between uupio, "ten thousand," and μvpíos, "infinitely numerous.' Homer has always μupíos both in the singular and in the plural, and always uses the word in the indefinite signification. With the definite value, as an indication of number, the singular is used with collective nouns in the historical writers; thus we have pupía doris in Xenophon for "ten thousand heavy-armed men;" similarly χιλίη ἵππος, “ a thousand cavalry,” in Herodotus; and διακοσία iTTOS, "two hundred horsemen," in Thucydides. Obs. 2 In statements of considerable and detailed numbers, it is common to begin with the digits and so ascend to the tens, hundreds, &c. Thus the number 63,974 will be expressed TérTapa Kai éẞdoμýkovтa καὶ ἐνακόσια καὶ τρισχίλια καὶ ἑξακισμύρια. But the reversed order is often adopted, especially when the sum consists of only two numbers; |