"You have seen my city."
Translation:Zobaczyłeś moje miasto.
The situation is a little bit difficult: in both Polish and English they are many words to describe the actions connected to seeing (e.g.: widzieć, patrzeć, zobaczyć, oglądać, ...; see, watch, look, observe, ...).
The dictionary sjp.pwn.pl gives the following definitions: "zobaczyć = 1. notice sth/sb while looking; 2. convince yourself personally about sth; 3. meet sb" and "widzieć = 1. see, i.e. see sth using the sense of sight; 2. have the ability to respond to light, the perception of people and things; [...] 4. meet sb; [...]". The verbs "widzieć, zobaczyć" have a different grammatical aspect in Polish (the first is imperfective (uncompleted action), the second perfective (completed action)). This feature can be expressed in English (using different tenses) but the correspondence isn't one-to-one and many things cannot be translated exactly. Moreover, I am no expert in grammar (neither Polish nor English). However, I'll try to explain something;).
Some examples first:
"Zobaczyłem ją, gdy wysiadła z autobusu. Teraz ją widzę" = "I saw/noticed her when she got off the bus. Now I see her (e.g. because we are standing on the same bus stop waiting for the next bus)"
"Widziałem ją gdy wysiadała z autobusu" = "I was seeing/observing her while she was getting off the bus (e.g. it took some time because there were many other passengers)". Note that also "wysiadła" changed to "wysiadała".
Now to the sentence in question:
"Zobaczyłyście moje miasto" - I think of the following translation in the first place: "You have been in my city (for some time) and have seen it (done some sightseeing etc.)".
"Widziałyście moje miasto (z samolotu)" = "You saw my city (from the airplane)" - clearly you saw it, but you didn't do any sightseeing. But it could also be a colloquial version of "Zobaczyłyście moje miasto"="You have been in my city (for some time) and have seen it (done some sightseeing etc.)".
Hope this helps. Comments are welcome!
PS: "Veni, vidi, vici" is in Polish: "Przybyłem, zobaczyłem, zwyciężyłem” not "Przybyłem, widziałem, zwyciężyłem”.
There is some resemblance to the pair of verbs:
"to hear" (słyszeć) and "to listen to" (słuchać).
You can see (widzieć) things when you are not blind,
just like you can hear (słyszeć), when you are not deaf.
Both types of perception are more or less passive.
You can really see/notice/become aware that you see (zobaczyć/zauważyć/uświadomić sobie, że się widzi)
when, all of the sudden and for some good or unknown reasons, your passive perception becomes conscious.