in a work entitled 'Prodromus of
Cosmographical Dissertations; containing the cosmographical mystery
respecting the admirable proportion of the celestial orbits, and the
genuine and real causes of the number, magnitude, and periods of the
planets, demonstrated by the five regular geometrical solids.' This
volume, notwithstanding the fanciful speculations which it contained,
was received with much favour by astronomers, and both Tycho Brahe and
Galileo encouraged Kepler to continue his researches. Galileo admired
his ingenuity, and Tycho advised him 'to lay a solid foundation for his
views by actual observation, and then, by ascending from these, to
strive to reach the causes of things.' Kepler spent many years in these
fruitless endeavours before he made those grand discoveries in search of
which he laboured so long.

The religious dissensions which at this time agitated Germany were
accompanied in many places by much tumult and excitement. At Gratz the
Catholics threatened to expel the Protestants from the city. Kepler, who
was of the Reformed faith, having recognised the danger with which he
was threatened, retired to Hungary with his wife, whom he had recently
married, and remained there for near twelve months, during which time he
occupied himself with writing several short treatises on subjects
connected with astronomy. In 1599 he returned to Gratz and resumed his
professorship.

In the year 1600 Kepler set out to pay Tycho Brahe a visit at Prague, in
order that he might be able to avail himself of information contained in
observations made by Tycho with regard to the eccentricities of the
orbits of the planets. He was received by Tycho with much cordiality,
and stayed with him for four months at his residence at Benach, Tycho in
the meantime having promised that he would use his influence with the
Emperor Rudolph to have him appointed as assistant in his observatory.
On the termination of his visit Kepler returned to Gratz, and as there
was a renewal of the religious trouble in the city, he resigned his
professorship, from which he only derived a small income, and, relying
on Tycho's promise, he again journeyed to Prague, and arrived there in
1601. Kepler was presented to the Emperor by Tycho, and the post of
Imperial Mathematician was conferred upon him, with a salary of 100
florins a year, upon condition that he should assist Tycho in his
observatory. This appointment was of much value to Kepler, because it
af