Not according to those books. It's been a long while since I read them but they were capable of locating islands far in front of them by reading changes in wave patterns. That's why I was wondering about the North Atlantic since there are so few islands there. I agree that European methods would not work well without sextants and math.
I think the empirical method is certainly more advanced in observing and interpreting one's environment, especially in relationship to the stars. But I also think it has serious limits. The sextant/math method can locate you anywhere on the planet independent of knowledge of islands.
So, while both methods are powerful, I think the sextant, clock methods are superior. I don't think the Europeans could have established world wide empires without their navigation methods.

__________________
1977 300d 70k--sold 08
1985 300TD 185k+
1984 307d 126k--sold 8/03
1985 409d 65k--sold 06
1984 300SD 315k--daughter's car
1979 300SD 122k--sold 2/11
1999 Fuso FG Expedition Camper
1993 GMC Sierra 6.5 TD 4x4
1982 Bluebird Wanderlodge CAT 3208--Sold 2/13