68] Sacrobosco, Purbach, Regiomontanus 87 



as a supplement to Sacrobosco's textbook, from which 

 this part of the subject had been omitted, but in part 

 also as a treatise of a higher order ; but he was hindered 

 in both undertakings by the badness of the only available 

 versions of the Almagest Latin translations which had 

 been made not directly from the Greek, but through 

 the medium at any rate of Arabic and very possibly of 

 Syriac as well (cf. 56), and which consequently swarmed 

 with mistakes. He was assisted in this work by his more 

 famous pupil John Miiller of Konigsberg (in Franconia), 

 hence known as Regiomontanus, who was attracted to 

 Vienna at the age of 16 (1452) by Purbach's reputation. 

 The two astronomers made some observations, and were 

 strengthened in their conviction of the necessity of astro- 

 Comical reforms by the serious inaccuracies which they 

 discovered in the Alfonsine Tables, now two centuries old ; 

 an eclipse of the moon, for example, occurring an hour late 

 and Mars being seen 2 from its calculated place. Purbach 

 and Regiomontanus were invited to Rome by one of the 

 Cardinals, largely with a view to studying a copy of the 

 Almagest contained among the Greek manuscripts which 

 since the fall of Constantinople (1453) had come into Italy 

 in considerable numbers, and they were on the point of 

 starting when the elder man suddenly died (1461). 



Regiomontanus, who decided on going notwithstanding 

 Purbach's death, was altogether seven years in Italy ; he 

 there acquired a good knowledge of Greek, which he had 

 already begun to study in Vienna, and was thus able to read 

 \ the Almagest and other treatises in the original ; he completed 

 I Purbach's Epitome of Astronomy, made some observations, 

 lectured, wrote a mathematical treatise * of considerable 

 merit, and finally returned to Vienna in 1468 with originals 

 or copies of several important Greek manuscripts. He 

 was for a short time professor there, but then accepted an 

 invitation from the King of Hungary to arrange a valuable 

 collection of Greek manuscripts. The king, however, soon 



* On trigonometry. He reintroduced the stne, which had been 

 forgotten ; and made some use of the tangent, but like Albategnius 

 ( 59 n -) did not realise its importance, and thus remained behind 

 Ibn Yunos and Abul Wafa. An important contribution to mathe- 

 matics was a table of sines calculated for every minute from o to 9 



