Herbert Weir Smyth, A Greek Grammar for Colleges

a. Objects well known: ὁ τῶν ἑπτὰ σοφώτατος Σόλων Solon the wisest of the Seven (Sages) P. Tim. 20d.

b Objects already mentioned or in the mind of the speaker or writer (the anaphoric article): εἶπον ὅτι τάλαντον ἀργυρίου ἕτοιμος εἴην δοῦναι . . . ὁ δὲ λαβὼν τὸ τάλαντον κ.τ.λ. I said that I was ready to give him a talent of silver . . . and he taking the talent, etc. L. 12.9-10.

c. Objects specially present to the senses or mind (the deictic article): ““λαβε τὸ βιβλίον” take the book” P. Th. 143c, ““βουλόμενος τὴν μάχην ποιῆσαι” wishing to fight the battle” T. 4.91. Hence the article is regularly used with demonstrative pronouns (1176).

N.—The foregoing (a - c) uses recall the old demonstrative force of the article. Words that ordinarily have no article may receive the article when this older force is present.

d. Objects particularized by an attributive or by a following description: ““ὁ δῆμος ὁ Ἀθηναίων” the people of the Athenians” Aes. 3.116, ““λέγε τὴν ἐπιστολήν, ἣν ἔπεμψεν” read the letter that he sent” D. 18.39. Cp. 1178 d.

e. Objects marked as usual or proper under the circumstances: τὸ μέρος τῶν ψήφων ὁ διώκων οὐκ ἔλαβεν the prosecutor did not get the (requisite) part of the votes D. 18.103.

f. Objects representative of their class (the distributive article, which resembles the generic use; often translated by a, each): ““ὑπισχνεῖται δώσειν τρία ἡμιδα_ρεικὰ τοῦ μηνὸς τῷ στρατιώτῃ” he promises to give each soldier three half-darics a month” X. A. 1.3.21. But the article may be omitted: καὶ εἵλοντο δέκα, ἕνα ἀπὸ φυ_λῆς and they chose ten, one from (each) tribe X. H. 2.4.23.