Help with translating a few sentences to English.

Hello all. I hope you’re doing well.

I was doing a lyric video yesterday and discovered a few Greek sentences that I have no clue how to translate into English. I’ve tried every single dictionary and Google Translate to get a grasp on it, but I just cannot.

Here’s the approximate text. Approximate because I can’t figure out how to type Omega (w) with a ~ above it and a , below it.
(I tried writing this myself.)
I’m quite sure that the ΰ is wrong but I found no way to put ~ above u as well. Mayhap it is ancient Greek?

Αριάνη γοΰν ή Μινωος θυγάτηρ έρωτιχώς τώ Θησεί διατεθείσα συμπράσσειν επαγγέλλεται έάν όμολογήση
γυναίχα αύτήν έξειν άπαγαών είς Αθήνας ύποθεμένου δέ έχείνου, λίνον είσιόντι Θησεί δίδωσι

Here’s the romanization:

Ariáni̱ goǘn í̱ Mino̱os thygáti̱r éro̱tichó̱s tó̱ Thi̱seí diatetheísa symprássein epangélletai éán ómologí̱si̱
gynaícha áf̱tí̱n éxein ápagaó̱n eís Athí̱nas ýpotheménou dé écheínou, línon eísiónti Thi̱seí dído̱si

Here’s the correct text. I noticed that the entire text is not showing, open the picture in a new tab and you should be able to read it all, or click the link.

Click to see the entire image.
Help with translating this to English would be greatly appreciated!

Thank you! ^-^