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Author Topic: THE RENAISSANCE  (Read 4733 times)
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« Reply #105 on: October 17, 2008, 08:59:43 pm »

Regiomontanus's history of mathematics is one that is founded in the practice of university mathematicians. Other than Diophantus (who, again, had only recently been discovered), the figures that Regiomontanus cites in his post-origin accounts of the mathematical disciplines were all known to contemporary mathematicians. Many of them were central to the traditional university mathematical curriculum and therefore to Regiomontanus's own education. He praises works like Euclid's Elements, Jordanus's De numeris datis, Jean de Murs's Quadripartitum numerorum, and Witelo's Perspectiva that, as mentioned above, had been widely used since the thirteenth and fourteenth centuries. He also mentions his contemporaries, men whose works had not yet had time to circulate extremely widely, but whom he saw as having made particularly important contributions to the mathematical arts, and also the great patrons of mathematics, men like Bessarion (his own patron) and Nicholas of Cusa. The history of mathematics, for Regiomontanus, is necessarily bound up with those figures who are central to the education and practice of his fellow mathematicians.

However, while Regiomontanus's vision of mathematics is grounded in university practice, it goes beyond it in scope. The authorities whom he praises most highly, Archimedes, Apollonius, and Ptolemy were known to university mathematicians but very rarely used. Latin translations of the works of Archimedes and of Ptolemy's Almagest were both available, and Archimedes, at least, was occasionally used.44 Apollonius had not been translated, although Witelo's Perspectiva shows at least a passing acquaintance [End Page 56] with his Conics.45 Regiomontanus, following the work of his mentor Peurbach, had recently completed an Epitome of the Almagest, but the scarcity of detailed knowledge of the Almagest even in Peurbach's Vienna can be seen in his Theoricae novae planetarum, written about a decade before he began work on the Epitome, in which Peurbach seems unaware, for example, of Ptolemy's solution for finding stationary points.46 By emphasizing the importance of Archimedes, Apollonius, and Ptolemy in addition to the traditional medieval sources, Regiomontanus advocated an augmentation of the standard practice of mathematics. The contemporaries for whom he had the highest praise, Peurbach and Bianchini, were men whom he knew shared his interests; Peurbach, of course, was his collaborator on the Epitome, and in 1463, Regiomontanus had begun corresponding with Bianchini over a variety of astronomical questions.47   
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