1. 385L33

2. Stations & Retrogression

4. Anaximander
6th cent. BCE
concentrism; symmetrical distances
Empedokles
ca. 450 BCE
reflected light; solar eclipse
Philolaos
5th cent. BCE
pyrocentrism; Counter-Earth
Plato
BCE
Spindle of Necessity; geocentric model
Eudoxus
BCE
27 spheres
Kallippos
BCE
34 spheres
Aristotle
BCE
56 spheres; 5th element (aither); Unmoved Mover

5. Eudoxan Spheres

6. Eudoxan Spheres SPHERE MOVEMENT/POSITION APPEARANCE D
planet on equator of D
W-E same speed as C
axis offset from axis of C
hippopede : retrogression C
E-W (axis perpendicular to axis of B)
stationary longitude
latitude oscillates at angle 2x offset between C and D B
W-E once/22 months on axis perpendicular to ecliptic
changes in speed
longitudinal movement opposite to zodiac
circuit through zodiac A
E-W once/24 hours on N-S axis
orbit around Earth

7. Eudoxan Spheres C + D

8. Eudoxan hippopede

10. Eudoxan Spheres

11. Eudoxus (410-355 BCE) CELESTIAL BODY EUDOXOS Moon 3 Sun Planets
Fixed Stars 1
TOTAL 27
• rational, geometric model
• accounts for observable movements assuming geocentricity and circularity
• failure to account for differences in brightness
• failure to account for some temporal irregularities in retrogression
• confirmation from contemporary geometric research on circles, spheres, angles
• nested spheres establish paradigm within which all subsequent research proceeds

12. CELESTIAL BODY
EUDOXOS
KALLIPPOS
Moon 3 5
Sun
Planets
5 x 4 = 20
3 x 5 (Mercury, Venus, Mars) + 2 x 4 (Jupiter, Saturn) = 23
Fixed Stars 1
TOTAL 27 34

13. CELESTIAL BODY
EUDOXOS
KALLIPPOS
ARISTOTLE
Moon 3 5
Sun
5 + 1 counter-sphere
Planets
5 x 4 = 20
3 x 5 (Mercury, Venus, Mars) + 2 x 4 (Jupiter, Saturn) = 23
counter-spheres (3 x 4 [Mercury, Venus, Mars] + 2 x 3 [Jupiter, Saturn] = 44
Fixed Stars 1
TOTAL 27 34 56

14. Aristotle ( BCE)
• confirmation of geocentricity and circularity • solution of physical problem of movement • counter-spheres added to communicate and “buffer” movements • mechanical vs. geometric model • physics of movement

15. Aristotelian Causes 1 (Artificial)
DEFINITION
EXAMPLE
Material
matter
wood
Formal
arrangement, appearance, shape
Efficient
agent
carpenter
Final/Telic
purpose
to support sitting

16. Aristotelian Causes 2 (Natural)
DEFINITION
EXAMPLE
Material
matter
biomass
Formal
arrangement, appearance, shape
Efficient
agent
nature
Final/Telic
purpose

17. Aristotelian Movement : Telic Cause
•Telic (or “final”) cause embodies aim (telos) towards which something either artificially or else naturally tends. •Chair = actualization (energeia) of wood’s (dynamis) = wood’s telic cause. •Tree = actualization (energeia) of acorn’s (dynamis) = acorn’s telic cause.

18. Aristotelian Movement : Actualization
• God perfect, complete, autonomous, self-actualized (energeia). • God embodies telos of the dynamis embodied in all things: perfect self-actualization (energeia). • Telic cause of all things = to become self-actualized = to become God. • Desire to become God  all movement.