Latittude

In c. 850 Arabs invented the astrolabe, which allows mariners to use celestial navigation to determine latitude.
The principle is still used in todays navigation (or at least taught in Nautical College). You measure the height (or altitude) using a sextant when the sun passes its highest point, and deduct that from 90° and add the sun's declination which can be found in the almanac (with date). Et voila: Lattitude!
Now just cross the ocean steering course 90 due East (or 270 due West). Keeping the sun at the same height would be the confirmation that you maintained the same lattitude. Currents or drift from the winds? Just steer a few degrees into the wind and check the next day what the result is.

This can also be done with stars at night.

You can download an instruction manual to make your own!