Greek Dative Case?
I noticed something today, (modern) Greek has 4 cases: Nom, Acc, Gen & Voc. But Ancient Greek had an extra Dative case, over time this was dropped, but for an indirect object, the add a sigma to the article of the Accusative case. I know this is a very small difference, but does anyone else think this should just be called the Dative case and say Greek has 5 still. This difference is small, but the difference between Nom and Acc in German is also really small so why not?
The dative case dropped out of Greek long ago, and its functions were mostly taken over by the genitive.
The dative case disappeared because of sounds changes that occurred regularly in Greek. The most common dative in Ancient Greek is -ῳ, but that little iota subscript stopped being pronounced fairly early on (before Roman times), so it became effectively just -ω. Some time later, the usual accusative ending was simplified from -ον to -o (the ν dropping away in most cases). Since Greek had by this time long lost vowel quantity distinctions due to the change to a stress accent, -ω and -ο were pronounced identically, and a dative that (in most cases) sounded exactly like the accusative couldn't be sustained as an independent case.
I'm not sure what you mean with "the add a sigma to the article of the Accusative case".
Do you mean something like Της δίνω ένα βιβλίο for "I give her a book"? Here, της is not an article; it's a pronoun. And the sigma at the end is only present in the feminine form; the masculine or neuter would be του.
And I'd call it the genitive case of the pronoun, not dative.
When you use a noun rather than a pronoun, the indirect object is usually marked with a preposition: Δίνω το βιβλίο στον πατέρα μου, for example, "I give the book to my father".
Ah, do you mean the στον? That's not a separate case, that's just a contraction of the preposition σε and the accusative article τον.
If you don't have a definite article, then you see the preposition, e.g. Δίνω το βιβλίο σε μια γυναίκα "I give the book to a woman" -- we don't say Δίνω το βιβλίο σμια γυναίκα. And in the indefinite plural, it's Δίνω τα βιβλία σε γυναίκες "I give the books to women", not Δίνω τα βιβλία σγυναίκες.
This is not a separate case; it's a preposition.