Abacus is a calculating tool, not a navigational instrument.

The astrolabe was used to measure the altitude of celestial bodies above the horizon, which was essential for determining latitude and longitude.

The compass is based on the principle that the angle of incidence is equal to the angle of reflection, which is a consequence of the law of sines.

The sundial was used to determine the time of day by measuring the angle of the sun's rays.

The Mercator chart was developed in the 16th century, after the time of ancient India.

The portolan chart was a navigational chart that showed the coastlines and harbors of a region, as well as the compass directions and distances between them.

The gnomonic chart was a navigational chart that was used to determine latitude and longitude by measuring the angles between the horizon and celestial bodies.

The nautical chart was a navigational chart that was used to measure the distance between two points by measuring the angles between the compass directions and the distances between them.

Quadrant is a mathematical tool used in surveying, not in navigation.

The quadrant was used to measure the altitude of celestial bodies above the horizon, which was essential for determining latitude and longitude.

Cross-staff is a navigational instrument used in astronomy, not in navigation.

The cross-staff was used to measure the altitude of celestial bodies above the horizon, which was essential for determining latitude and longitude.

Backstaff is a navigational instrument used in astronomy, not in navigation.

The backstaff was used to measure the altitude of celestial bodies above the horizon, which was essential for determining latitude and longitude.

Nocturnal is a navigational instrument used in astronomy, not in navigation.

The nocturnal was used to calculate the time of day by measuring the angle between the horizon and the stars.