In the Last part of Astronomia Nova (Ch. 69) Kepler describes a way the ancient astronomers might did it. Kepler suspects this way Ptolemy was using but he is not sure. The process can be generally described as such:

1. Using the Merdian altitudes one can infer where are the equinoxes (at least in time); (though Ptolemy might be using Alexandrian armillaries)

2. Once The obliquity of Earth was known, one could use the declination (direct from observation of Merdian altitude) to know the elongation (ecliptic longitude distance) of the Sun from the equinox. this is done by simple spherical trigonometry calculation.

3. One can during the day find the angular distance between the Sun and the Moon.

4. then at night, we have the Moon and can see the distance of the Moon from the fixed stars that are visible at night say star X.

5. Now we basically have everything. we have the distance X-Moon; Moon-Sun; Sun-equinox. So we have the angular distance between X and the equinox.

It should be stressed that the ancient - up until the great Tycho Brahe had severe issues in their Theory of Sun. Tycho got wrong the location of the Sun in about 7 minutes of arcs! this is mainly because of refraction and parallax issues which they knew existed but took the wrong quantities.

In the Last part of Astronomia Nova (Ch. 69) Kepler describes a way the ancient astronomers might did it. Kepler suspects this way Ptolemy was using but he is not sure. The process can be generally described as such:

1. Using the Merdian altitudes one can infer where are the equinoxes (at least in time); (though Ptolemy might be using Alexandrian armillaries)

2. Once The obliquity of Earth was known, one could use the declination (direct from observation of Merdian altitude) to know the elongation (ecliptic longitude distance) of the Sun from the equinox. this is done by simple spherical trigonometry calculation.

3. One can during the day find the angular distance between the Sun and the Moon.

4. then at night, we have the Moon and can see the distance of the Moon from the fixed stars that are visible at night - say star X.

5. Now we basically have everything. we have the distance X-Moon; Moon-Sun; Sun-equinox. So we have the angular distance between X and the equinox.

It should be stressed that the ancients - up until the great Tycho Brahe -had severe issues in their Theory of Sun. Tycho got wrong the location of the Sun in about 7 minutes of arc at the equinoxes; this is mainly due to refraction and parallax issues which they knew existed but took the wrong quantities.