ty-three. This series of educational opportunities will be
surprising only to those who do not know educational realities at the
beginning of the fifteenth century. There has never been a time when a
serious seeker after knowledge could find more inspiration. On his
return to Germany, Father Krebs became canon of the cathedral in
Coblenz. This gave him a modest income, and leisure for intellectual
work which was eagerly employed. He was scarcely more than thirty when
he was chosen as a delegate to the Council at Basel. After this he was
made Archdeacon of the Cathedral of Luettich, and from this time his rise
in ecclesiastical preferment was rapid. He had attracted so much
attention at the Council of Basel that he was chosen as a legate of the
Pope for the bringing about certain reforms in Germany. Subsequently he
was sent on ecclesiastical missions to the Netherlands, and even to
Constantinople. At the early age of forty he was made a Cardinal. After
this he was always considered as one of the most important consultors
of the Papacy in all matters relating to Germany. During the last
twenty-five years of his life in all the relations of the Holy See to
Germany, appeal was constantly made to the wisdom, the experience, and
the thoroughly conservative, yet foreseeing, judgment of this son of the
people, whose education had lifted him up to be one of the leaders of
men in Europe.

It was during this time that he wrote most of his books on mathematics,
which have earned for him a prominent place in Cantor's "History of
Mathematics," about a score of pages being devoted to his work. Much of
his thinking was done while riding on horseback or in the rude vehicles
of the day on the missions to which he was sent as Papal Legate. He is
said to have worked out the formula for the cycloid curve while watching
the path described by flies that had lighted on the wheels of his
carriage, and were carried forward and around by them. His scientific
books, though they included such startling anticipations of Copernicus'
doctrines as we have already quoted (Copernicus did not publish the
first sketch of his theory for more than a quarter of a century after
Cusanus' death), far from disturbing his ecclesiastical advancement or
injuring his career as a churchman, seem actually to have been
considered as additional reasons for considering him worthy of
confidence and consultation.

As the result of his careful studies of conditions in Germa