Herbert Weir Smyth [n.d.], A Greek Grammar for Colleges; Machine readable text [info] [word count] [Smyth].
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1125 THE ARTICLE WITH NUMERALS

The article may be used with cardinal numerals

a. When the numeral states the definite part of a whole (expressed or understood): ἀπῆσαν τῶν λόχων δώδεκα ὄντων οἱ τρεῖς of the companies, numbering twelve (in all), there were absent three X. H. 7.5.10, εἷς παρὰ τοὺς δέκα one man in (comparison with) ten X. O. 20.16, τῶν πέντε τὰ_ς δύο μοίπα_ς two fifths T. 1.10, δύο μέρη two thirds 3. 15. (The genitive is omitted when the denominator exceeds the numerator by one.)

b. When the numeral is approximate: ἔμειναν ἡμέρα_ς ἀμφὶ τὰ_ς τριά_κοντα they remained about thirty days X. A. 4.8.22, γεγονότες τὰ πεντήκοντα ἔτη about fifty years of age X. C. 1.2.13.

c. When the number is used abstractly (without reference to any definite object): ὅπως μὴ ἐρεῖς ὅτι ἔστιν τὰ δώδεκα δὶς ἕξ beware of saying 12 is twice 6 P. R. 337b.

N. Ordinals usually omit the article and regularly do so in statements of time in the dative ( cross1540): δευτέρῳ μηνὶ τὴν πόλιν ἐτείχιζον in the second month they fortified the city T. 8.64.

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Herbert Weir Smyth [n.d.], A Greek Grammar for Colleges; Machine readable text [info] [word count] [Smyth].
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