Columbus and Celestial Navigation used a Astrolabe and Dead reckoning tools.
Just think of taking a curse with Columbus in 1492
.At this time there was no real time keeping for Longitude.
By this time they figure out latitude using a ASTROLABE and the sun move 23?° up and down in 365 days.
?The Accuracy was lest than ?° off or (17 NM , 19.7 miles , 34.5KM) Even today's standards that is close.The main way for Longitude was to use Dead Reckoning a hourglass and rope with knots at given spacing and board at end and a Compass.
They plot out on paper there course. If they was off on ladatude correction was made. Depending the group measuring the spoed and number of course changes made per day and cross current errors.Remember at this they did not of navigating on a round ball aka earth too.
This work very well till we had time accuracy keeping and one spot on earth?
?zero.Here is the simple way of finding LONGITUDE.Solar time different from your location and Greenwich Time in hours?X?15 is LONGITUDE?.You are?10? hours?in time from Greenwich times?15 = 157.5° or 157° 30'
A sundiel could be used for time .
LATITUDE
Some Astrolabe has a disk to adjust for the day year .
Depending on the that mader of the astrolabe is accuracy. Most re very good.
A sextant takes in more factors but still at end simple except you chart for each day and you correction for very accurate angle