V THE NUMBERS IN GREEK AND LATIN, AND THEIR RELATIONS NUMBERS are three, Dionysius Thrax tells us, Singular (évikós), Dual (Svïkós), Plural (πλŋovνTɩKós). But there are singular expressions used also for many, e.g. δῆμος, χορός, ὄχλος; and plurals used both for singulars and duals; for singulars, e.g. 'Avai, nßai; and for duals, e.g. åμpóтepoɩ (p. 30, Uhlig). Such is the statement about numbers in our oldest grammar; but it is far from being full or exhaustive. Let us state the matter a little more fully and in detail. (1) The singular is used for the plural. Dionysius's examples are all nouns of multitude, where no one would dream of counting the units, or treating them as individuals, e.g. váμpos or váμalos 'sand'. Here the Greek usually has either the singular or the plural with the same meaning; e.g. λaós or λaoí; while Latin uses the singular populus. In English we use now the singular, now the plural, saying 'wheat' and 'barley', but 'oats' and 'pease'. When Virgil ventured in imitation of aλpira to write hordea 'barleys', he met with Bavius's reproach: Hordea qui dixit, restat ut tritica dicat, a reproach fully justified by Latin idiom. (2) The plural is used for the singular. Dionysius's examples for Greek are names of cities, like Athens or Thebes, and Latin gives us similar examples in Veii, Gabii, Corioli. The same is true of festivals held on a single day like Θεσμοφόρια, Διονύσια, Ελευσίνια, Saturnalia, Kalendae, Idus. (3) The plural is used for the dual; indeed Homer uses the plural dolí instead of dúw (Il. 5. 206), and in the first Iliad Achilles greets the two heralds: xaípete, kýpukes (v. 334). After Aristotle the dual passes out of use in Greek, and for a pair the plural is regularly used. In Latin duo and ambo are the only two duals recognized by the Romans, and for the remaining cases of these words plural forms are used, like ambos or duobus. Speaking generally, when the dual goes out of use the plural takes its place. (4) The dual is used for the plural. In Greek for several pairs we often find the dual used, and not the plural, as in: oi 8 åμa távtes ép ἵπποιϊν μάστιγας ἄειραν (II. 23. 362) and they all with one accord raised their whips upon their teams'. Dionysius does not proceed to give us this use, probably from a natural piety. Zenodotus, the founder of the Alexandrian school of grammarians, maintained that Homer used the dual for the plural; but Aristarchus of Samothrace, the teacher of Dionysius, wrote in refutation of this a treatise now lost. No doubt he tried to show that in all examples of this use cited by Zenodotus there was an idea of pairing involved that justified the use of the dual. But the syntax of åλóvre with yévŋole in : μήπως, ὡς ἀψῖσι λίνου ἁλόντε πανάγρου ἀνδράσι δυσμενέεσσιν ἕλωρ καὶ κύρμα γένησθε (Ιl. 5. 487–8) seems to involve no such idea of pairing. In Latin while octo and viginti, old duals, are used as plurals, this idea of pairs is primarily involved, though no longer felt. But equae 'the mares', primarily a dual (= Skt. açve), is used for any number of mares. (5) We have examined in the previous chapters a number of cases where in Latin the singular is evidently used for the dual. This use seems rarer in Greek; but where in Skt. we have nāsā 'the nose', a duale tantum, in Greek we find pís or pîves, a singular or a plural. (6) The dual is used for the singular, but not in Greek or Latin. But in Latin we find plurals used for older duals in use for the singular. In Sanskrit we find two duals used for two related singulars in: Mitrā Varunā. So in: Lugete o Veneres Cupidinesque (Catull. 3. 1) we have two plurals used similarly for two related singulars. I might proceed to ask how far we have reason to believe that the dual number is coeval with the singular and the plural. The dual seems to have existed in all branches of the Indo-Germanic family of languages; and so we have a right to consider it an inflexion of the primitive Indo-Germanic. But probably it was much later and more imperfect in its development than the singular and the plural. The inflexions for the dual of nouns, pronouns, and verbs seem to show from their lack of development that the dual was later, and was never in regular use even for pairs. Its use is most fully developed and most regular in Sanskrit and Gothic, both artificial or book languages as we know them. VI THE DUAL IN LATIN THAT the dual existed in Latin, is recognized by Donatus and his school. In Donatus's Ars we read: Est et dualis numerus, qui singulariter enuntiari non potest, ut hi ambo, hi duo (IV. 376. 23, K.). Servius, in his commentary to Donatus's Ars, adds that this is why they are irregular in declension; they have dual forms for the nominative, and plural for the oblique cases (IV. 408. 17, K.). To duo and ambo Sergius adds uter and neuter (IV. 540. 7, K.). Later anonymous grammarians under the influence of philosophy seem disinclined to accept the dual: quia non est in natura rerum hic tertius numerus (Ars Anon. Bern., Suppl. 84. 18, K.); sed hunc non recipimus, quia, qui singularitatem excedit, in pluralitate deprenditur (Comm. Einsidl. in Don. Artem, Suppl. 240. 14, K.). The earlier Roman grammarians like Donatus were fortunately free from this influence, and were determined in their view by the form of duo and ambo; for duo corresponds exactly to the Greek Súo, and ambo, mutatis mutandis, to aμpw. Duo is shortened from the older duō by the law of brevis brevians, the same that gives us beně and malě. Porphyrio's note to Hor. Sat. 2. 3. 248 is: ludere par impar, uni dui (Cod. Med.); so in the fifth century of our era duo seems to have developed a plural dui, just as dúo developed dolí. The & in aμow is for an older bh (cf. Skt. ubhau); the Roman, who could not aspirate as did the Greek, and down to 150 B. C. wrote Corintus as he pronounced it, for bh wrote b in ambo. But the Latin grammarians had a further motive for emphasizing the fact that they found a dual in Latin. Latin grammatical studies, Varro tells us, begin in 157 B. C., when Crates of Mallos, sent to Rome as ambassador from King Attalus, while taking a walk on the Palatine, fell and broke his leg. During the inactivity consequent on his accident, he found time to give some attention to the Latin language, which he decided was a depraved derivative of Greek. The circle of the Scipios and the Aemilii eagerly adopted the notion that associated their language with Greek; and grammatical studies of this tendency came into fashion. But a century later Romans were no longer so disposed to accept this view; and it was to refute one Hypsicrates, who wrote from this standpoint, that Varro composed his De Lingua Latina. That Latin is an independent language, he maintains, and points to the number of Latin cases, one more than in Greek, to prove his point. All the older Latin grammarians follow him in this endeavour to show that Latin is at least as rich as Greek in grammatical inflexions. The two forms ambo and duo seem to some of them a narrow basis for their claim of a Latin dual; so we read in Cledonius: et communis est numerus, qui et dualis dicitur apud Graecos, ut species, facies, res (V. 10. 19, K.). In assigning genders, when a word had the same form for the male and the female, as πos or homo, the Greeks and Romans agreed that its gender was 'common'. Cledonius finds that species, facies, res have the same form for the singular and the plural, and so sets up a 'common number', equivalent to the Greek dual, he tells us. In this he seems to have found no following. But the Greek verb also has forms for the dual distinct from the plural forms; and so some Romans claimed that forms like legere, fecere, conticuere were duals (vide Cledonius, V. 60. 6, K.). All Latin usage is against this; Donatus denies that they are duals, and Macrobius, to prove they are not, cites Virgil's conticuere omnes (Aen. 2. 1), and una omnes fecere pedem (5. 830). In the Commentum Einsidlense (Suppl. 256. 3, K.) we find legere confused with the infinitive legere: dicimus enim legere volo et legere volumus in singulari numero et in plurali;-another attempt to establish a common number as a dual. Legēre seems the old and genuine form of the third plural perfect, which later, on analogy of the present, became legerunt. But our great Latin grammarians like Vossius and Ruddiman make no mention of a Latin dual. They seem to have held the grammar of Priscian to be of higher authority than that of Donatus; and Priscian knows nothing of a Latin dual; nor do his sources, Charisius and Diomedes. In A.D. 327 Constantine removed the seat of empire from Rome to Byzantium; and at once the Greeks, who have henceforth to administer Latin law, feel the need of a knowledge of the Latin language. To satisfy this the great grammars of Charisius and Diomedes are composed; and as both are intended to teach Greeks Latin, both state with emphasis that Latin, unlike Greek, has no dual; and Priscian, who like them composed his great work in Constanti nople about 150 years later, follows them in this. But Donatus and the older grammarians were right in their claim that there was a Latin dual, and that traces of this number and of forms arising from its presence still exist in Latin. We may review briefly these traces. Like ambo and duo, octo is the Greek OKTÓ, the Sanskrit astau, which Fick thought meant primarily the two points', i. e. the two hands held out with the thumbs folded into the palms. So viginti is the two tens, like the Greek elkoot (old Fíkar) and the Sanskrit vinçati; and in all three the ending is the regular ending of the neuter dual in Sanskrit. Wilamowitz thinks that in the inscription: M. C. Pomplio No. f. dedron Hercole, Pomplio is a dual, and his view is favoured by Leo (Pl. Forsch. 333); and Schulze thinks that in: Q. K. Cestio Q. f. Hercole donu dedero (C. I. L. 14. 2891) Cestio is a dual. The ending o found in ambo, octo, Pomplio, Cestio, seems the ending in iπ and in the Skt. açvau, where the u seems a reduction of the vi- in viginti and means 'two'. It is the root of the Skt. vidya 'knowledge' (cf. scio and descisco), and of the old verb vido found in the compound divido. When we read in Horace : Hoc iter ignavi divisimus, altius ac nos the translation of divisimus induced by its opposition to unum, 6 we Sommer (Lat. Laut- u. Formenlehre, 424) explains ū in neuters of the fourth declension as got by analogy from the ū in genu and cornu, which are old duals like the Skt. sūnū 'the two sons'. Cornu die beiden Hörner das Gehörn das Horn. So in English, speaking of the two knees, we use the phrase 'to bow the knee'. He thinks genūs is for an older genuos, where the ending os is that of the gen.-abl. dual in Skt. Brugmann is inclined to agree that genūs is the old genitive dual, but refuses to accept genu as a nominative dual till he has more evidence that sūnū is an IndoGermanic form. It is interesting to meet this fresh case of a dual passing into the singular. But the great majority of Latin forms once dual, if we follow Brugmann, now appear as plurals. Equae is the exact equivalent phonetically of the Skt. açve, and meant primarily 'the pair of mares'; Oúpa is primarily 'the pair of doors', and corresponds to a Latin forae still found in the acc. foras and the abl. foris. The later development of the dual in Greek, rà κópa, which has nothing to |