MATH-EM ATICAL SCIENCES. 93 







the school of Florence. Dugomari, called Paul the Geometer, and Abbaco 

 contributed simultaneously to the progress of the exact sciences, but none of 

 their pupils were capable of taking their place. 



Mathematics were but little cultivated in France, though in the fourteenth 

 century may be mentioned Jean de Lignieres, whom a chronicler calls "the 

 restorer of the science of the stars," and Jean des Murs, canon of the 

 Cathedral of Paris, who compiled some valuable works on Arithmetic. 

 Bonnet de Lates, a physician in Provence, conceived the idea of an astro- 

 nomical ring for measuring the height of the sun and the stars (Fig. 68). 

 This mathematician failed, however, to guard himself from the errors of 

 contemporary science, and his weighty study of astronomy did not save him 

 from making predictions based upon the conjunctions of the planets and so 

 forth, 



During the Italian Renaissance. mathematics were not neglected, and they 

 were taught with success during' the fifteenth century at Rome, Naples, 

 Padua, Bologna, Pisa, and more especially at Florence. They were at that 

 time almost entirely extricated from the dangerous illusions of astrology, 

 and no longer involved noble minds in the fatal paths of doubt and heresy. 

 They were professed, moreover', by some of the principal doctors of the 

 Church, and were in a certain degree honoured by the direct protection of 

 the Holy See, when ^35neas Sylvius Piccolomini, one of the first mathema- 

 ticians of his century, was elected Pope, with the title of Pius II. (1458 

 1464). Pope Pius II. was a man of general learning, but his favourite 

 study was that of cosmography. At the same time, Cardinal Nicholas de 

 Cusa, his rival in learning, found time, while fulfilling his diplomatic 

 functions at the Court of Rome, to write works on Mathematics, Geometry, 

 and Astronomy, in which he maintained the system of the earth's rotation 

 around the sun, and admitted in principle the plurality of worlds, two 

 centuries before Galileo. 



The example of Pius II. induced his successors, Paul II. and Sixtus IV., 

 to favour the exact sciences. It was Sixtus IV. who summoned to Rome the 

 celebrated Konigsberg astronomer, Johann Miiller, called Regiomontanus, who 

 had been recommended to him by Cardinal Bessarion. Regiomontanus, the 

 most celebrated pupil of G. Purbach, had already obtained a great reputation 

 in Italy, whither he accompanied Cardinal Bessarion in 1463. The course 

 of astronomy which he commenced at Padua in that year attracted an 



