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 this age, and was zealously studied even by men of eminence and mathematical ability. The army of circle-squarers became 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 $$\scriptstyle{\pi}$$ to 15, the latter to 35, places. The value of $$\scriptstyle{\pi}$$ 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 28 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