sun in a focus of each.[2]

It is often difficult to define the boundaries between fancies,
imagination, hypothesis, and sound theory. This extraordinary genius
was a master in all these modes of attacking a problem. His analogy
between the spaces occupied by the five regular solids and the
distances of the planets from the sun, which filled him with so much
delight, was a display of pure fancy. His demonstration of the three
fundamental laws of planetary motion was the most strict and complete
theory that had ever been attempted.

It has been often suggested that the revival by Copernicus of the
notion of a moving earth was a help to Kepler. No one who reads
Kepler's great book could hold such an opinion for a moment. In fact,
the excellence of Copernicus's book helped to prolong the life of the
epicyclical theories in opposition to Kepler's teaching.

All of the best theories were compared by him with observation. These
were the Ptolemaic, the Copernican, and the Tychonic. The two latter
placed all of the planetary orbits concentric with one another, the
sun being placed a little away from their common centre, and having no
apparent relation to them, and being actually outside the planes in
which they move. Kepler's first great discovery was that the planes
of all the orbits pass through the sun; his second was that the line
of apses of each planet passes through the sun; both were
contradictory to the Copernican theory.

He proceeds cautiously with his propositions until he arrives at his
great laws, and he concludes his book by comparing observations of
Mars, of all dates, with his theory.