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Accusative: reference as modifier
διὰ μέσου δὲ τῆς πόλεως ῥεῖ ποταμὸς Κύδνος ὄνομα, εὖρος δύο πλέθρων
‘’ (Xen. Anab. 1.2.23)
The accusative signals the quality or entity to which a noun refers, particularly with regard to its size, name or provenance.
The following accusatives are often used as accusatives of reference, usually without the article: ὄνομα ‘by name’, γένος ‘by family’, ἀριθμόν ‘in number’, μέγεθος ‘in size’, εὖρος ‘in breadth’, ὕψος ‘in height’, μῆκος ‘in weight’.
ὦ πάτερ, ἦ τοι σεῖο μέγα κλέος αἰὲν ἄκουον,
χεῖράς τ’ αἰχμητὴν ἔμεναι
Father, I have always heard of your great fame, of being a lance bearer, skillful by hand. [provisional translation]
δωρεὰν δ’ εἰληφότα ὁδοῦ τῆς εἰς Ῥώμην τριακοσίων ταλάντων ἀριθμόν
... and for his journey to Rome he had received a reward of thirty talents in number.