most formidable during the seventeenth century. Among the first to revive this problem was the German Cardinal Nicolaus Cusanus (died 1464), who had the reputation of being a great
logician. His fallacies were exposed to full view by Regiomontanus.
As in this case, so in others, every quadrator of note raised up an opposing mathematician: Orontius was met
by Buteo and Nonius; Joseph Scaliger by Vieta, Adrianus
Romanus, and Clavius; A. Quercu by Peter Metius. Two
mathematicians of Netherlands, Adrianus Romanus and Ludolph
van Ceulen, occupied themselves with approximating to the ratio between the circumference and the diameter. The former carried the value to , the latter to , places. The
value of is therefore often named "Ludolph's number." His
performance was considered so extraordinary, that the numbers were cut on his tomb-stone in St. Peter's church-yard, at Leyden. Romanus was the one who propounded for solution that equation of the forty-fifth degree solved by Vieta. On receiving Vieta's solution, he at once departed for Paris, to make his acquaintance with so great a master. Vieta proposed to him the Apollonian problem, to draw a circle touching
three given circles. "Adrianus Romanus solved the problem by the intersection of two hyperbolas; but this solution did not possess the rigour of the ancient geometry. Vieta caused him
to see this, and then, in his turn, presented a solution which had all the rigour desirable."25 Romanus did much toward simplifying spherical trigonometry by reducing, by means of
certain projections, the cases in triangles then considered to only six.
Mention must here be made of the improvements of the Julian calendar. The yearly determination of the movable
feasts had for a long time been connected with an untold
amount of confusion. The rapid progress of astronomy led to the consideration of this subject, and many new calendars were proposed. Pope Gregory XIII. convoked a large number of mathematicians, astronomers, and prelates, who decided upon the adoption of the calendar proposed by the Jesuit Lilius Clavius. To rectify the errors of the Julian calendar
it was agreed to write in the new calendar the 15th of October immediately after the 4th of October of the year 1582. The Gregorian calendar met with a great deal of opposition both among scientists and among Protestants. Clavius, who ranked high as a geometer, met the objections of the former most ably and effectively; the prejudices of the latter passed away with time.
The passion for the study of mystical properties of numbers descended from the ancients to the moderns. Much was written on numerical mysticism even by such eminent men as Pacioli and Stifel. The Numerorum Mysteria of Peter