Gothic þau, English the

I'm a native Russian speaker and I couldn't select an appropriate Russian translation for a German word "doch" for a long time. When one say "nein" and the other say "doch".

I chose "definitely" translation.

Then I found out, that German "doch" and Gothic "þauh" are cognates.
Then I checked my "definitely" translation for Gothic. In my opinion, my variant is appropriate for Gothic also.
http://www.wulfila.be/gothic/browse/search/?find=%C3%BEauh&mode=5
Then I found out, that Gothic þauh = þau + uh.
Then I checked my "definitely" translation for Gothic þau. In my opinion, my variant is appropriate for Gothic þau also.
http://www.wulfila.be/gothic/browse/search/?find=+%C3%BEau&mode=5
Then I thought of an English definitive article "the" and Gothic "þau".

Could they be cognate?

i.e.

Mother: You will go to bed at nine o'clock
Son: nein (no)
Mother: doch (definitely)

Mother has already defined that time in advance and it is beyond doubt.