The Flat Earth; Increase of Spheres; Eccentric Spheres

Flat Earth

Before the Concentric Spheres system was taught in the world, the earth was regarded as a vast and irregular plain, surrounded on all sides by the ocean.

• Its roots extended infinitely deep
• The sky was as a solid hemisphere, which covered the earth, and united with the ocean at the extremity of the horizon.
• The Sun, the Moon, and all the heavenly bodies rose out of the eastern, climbed up the convex side of the heavens, and descended again into the western ocean.
• The Earth was surrounded by the elements of Air and Ether, and covered by 8 polished and cristalline Spheres, each of which was distinguished by one or more beautiful and luminous bodies. These revolved around their common centre, by varied but equable proportionable motions.

This was believed by:

• Xenophanes, the founder of the Eleatic philosophy
• after that of the Ionian and Italian schools, the earliest that appeared in Greece.
• Thales of Miletus too, who, according to Aristotle, represented the Earth as floating upon an immense ocean of water

The beauty of this system:

• gave to Plato the notion of a harmonic proportion hidden in the motions and distances of the heavenly bodies.
• suggested to the earlier Pythagoreans the celebrated fancy of the Music of the Spheres
  • This is a wild and romantic idea

Eudoxus was the friend and auditor of Plato. He wanted to remedy the defects in the motions of the Celestial Spheres by increasing their number.

• He gave 4 spheres to each planet
  • 1 in which the planet itself revolved
  • 3 others above it.

The motion of the Fixed Stars being perfectly regular, one Sphere he judged sufficient for them all.

This led to a total of 27 Celestial Spheres.

Callippus, though somewhat younger, the cotemporary of Eudoxus, found that even this number was not enough to connect together the vast variety of movements which he discovered.

Aristotle therefore increased it to 34.

Observers discovered still new motions, and new inequalities, in the heavens. And so 22 were added, which increased their number to 56.

By the 16th century, Fracostorio increased the number of 72 Celestial Spheres, but even that was not enough.

The System of Eccentric Spheres and Epicycles

Not long after Aristotle, Apollonius invented the more unnatural System of Eccentric Spheres and Epicycles to remedy the problems with the Concentric Spheres.

• This was perfected by Hipparchus.
• Since then, it had been delivered down to us by Ptolemy.

The irregular real speeds of the bodies could not match the regular spheres when viewed from their own centers. So they invented for each of them, the Equalizing Circle. From its centre they should all appear perfectly equable.

They so adjusted the velocities of these Spheres. Their own revolutions might appear irregular when surveyed from its own centre. But there would be a new point within its circumference from where its motions would appear to cut off, in equal times, equal portions of the Circle, of which that point was the centre.

The invention of this Equalizing Circle proves that the tranquillity of the imagination is the ultimate end of philosophy.