find a law
connecting the distances and periods of the planets, but without success
at that time, and only desisted when by unconsciously arguing in a
circle he appeared to get the same result from two totally different
hypotheses. He sent copies of his book to several leading astronomers,
of whom Galileo praised his ingenuity and good faith, while Tycho Brahe
was evidently much struck with the work and advised him to adapt
something similar to the Tychonic system instead of the Copernican. He
also intimated that his Uraniborg observations would provide more
accurate determinations of the planetary orbits, and thus made Kepler
eager to visit him, a project which as we shall see was more than
fulfilled. Another copy of the book Kepler sent to Reymers the Imperial
astronomer with a most fulsome letter, which Tycho, who asserted that
Reymers had simply plagiarised his work, very strongly resented, thus
drawing from Kepler a long letter of apology. About the same time Kepler
had married a lady already twice widowed, and become involved in
difficulties with her relatives on financial grounds, and with the
Styrian authorities in connection with the religious disputes then
coming to a head. On account of these latter he thought it expedient,
the year after his marriage, to withdraw to Hungary, from whence he sent
short treatises to Tuebingen, "On the magnet" (following the ideas of
Gilbert of Colchester), "On the cause of the obliquity of the ecliptic"
and "On the Divine wisdom as shown in the Creation". His next important
step makes it desirable to devote a chapter to a short notice of Tycho
Brahe.

[Footnote 2: Since the sum of the plane angles at a corner of a regular
solid must be less than four right angles, it is easily seen that few
regular solids are possible. Hexagonal faces are clearly impossible, or
any polygonal faces with more than five sides. The possible forms are
the dodecahedron with twelve pentagonal faces, three meeting at each
corner; the cube, six square faces, three meeting at each corner; and
three figures with triangular faces, the tetrahedron of four faces,
three meeting at each corner; the octahedron of eight faces, four
meeting at each corner; and the icosahedron of twenty faces, five
meeting at each corner.]

CHAPTER III.

TYCHO BRAHE.

The age following that of Copernicus produced three outstanding figures
associated with the science of astronomy, then reaching the close of
wha