We know of at least three tools Ptolemy used in his calculation of the position of the Sun, the planets, and the stars.
To measure the Sun’s position, he probably used a quadrant.
A quarter of a circle was ruled on a square board and a special line was attached to make sure it was held vertically.
There was a pivoting arm on the board with open sights. This arm was moved against the quadrant to determine the Sun’s height above the horizon.
A device called an armillary sphere was used for the planets. The sphere contained a series of circles.
These circles corresponded to the ancients’ view of the heavens as a series of circles surrounding Earth, each holding the planets as they revolved around Earth. The tool was used to give the planets a celestial latitude and longitude.
Ptolemy actually invented a tool to measure the position of the stars Ptolemy’s rules.
A stick was held vertically and a line attached to keep the stick straight. A pivoting arm with open sights was attached to one end. The other end had a pivoting board with movable pegs in it.
The pegs could be set at previously measured points to calculate the positions and movements of stars.