Here’s how you can categorize each of the items:
Aristotle:
- Geocentric
- Planets fixed on nested spheres
Ptolemy:
- Planets fixed on epicycles
- Accurately predicted the positions of the planets
Both (or could be related to both):
- Geocentric (this concept is often associated with Aristotle but was also part of Ptolemy's model)
So the final categorization is:
- Planets fixed on nested spheres – Aristotle
- Geocentric – Aristotle (Also related to Ptolemy)
- Planets fixed on epicycles – Ptolemy
- Accurately predicted the positions of the planets – Ptolemy