518 Prof. De Morgan ofi the almost total Disappearance 



able, if we remember that he held the chair of mathematics at 

 Wittemberg, in which Luther had very lately taught theology, 

 and burned the pope's bull, and in which Melancthon actually 

 taught Greek. Riccioli very gravely informs us that Rheticus 

 received a supernatural punishment for his presumption. 

 "While he was puzzling himself about the motion of Mars, he 

 invoked his genius or guardian angel to help him out of the 

 difficulty : the angel accordingly lifted him up by the hair of 

 his head to the roof and threw him down upon the pavement, 

 saying with a bitter laugh, " That *s the way Mars moves." 

 Kepler, it seems, had heard this story with such evidence as 

 induced him to suppose that Rheticus must have knocked his 

 head against the wall in the agitation of his spirits. Riccioli 

 does not feel himself at liberty to make any other mention of 

 him, and adds damnatus auctor to his name, in a list in which 

 Copernicus himself figures without remark : and Clavius, in 

 the diffuse trigonometry attached to the edition of Theodosius, 

 does not even introduce his name. The Jesuit Blancanus, 

 also, in his list of mathematicians, excludes Rheticus altogether, 

 though he was a contemporary of the Opus Palatinuniy and 

 though he admits Copernicus. 



The works of Rheticus are accordingly very scarce ; and 

 it can be no matter of surprise that one of them, and perhaps 

 more, should have entirely slipped out of notice. Even the 

 second edition of Copernicus, Basle, 1566, which was edited 

 by Rheticus, is much more scarce than the first. 



The early history of trigonometrical tables, as given, may 

 be thus summed up. Tables of sines, which were substituted 

 for Ptolemy's chords by Albategnius, were published, to every 

 minute, from Regiomontanus* (who died in 1476), and also 

 by Apian, both in 1533. Regiomontanus used tangents, as 

 the Arabs had done before him, and there is a table, to de- 

 grees only, in a work of his published by Reinhold in 1561. 

 This same Erasmus Reinhold had printed tangents of every 



* Such is the statement : but on examining the work on triangles by 

 Regiomontanus, in which these sines are said to occur, and which was 

 published in 1533, I cannot find any table at all. But Apian published 

 two tables of sines : one in the Introductio Geographica, 1533, and another 

 in the Instrumentum primi mobilis, 1534. There is a table of sines in the 

 TabulcE Directionum, 1552, and another in the second edition of the work 

 De Triangulis, Basle, 15(31, folio. And in the catalogue of De Thou's 

 library,and in Niceron's list, Murhard's catalogue, and Kiistner's history, is 

 mentioned the following work, " Joh. Regiomontani compositio tabularum 

 Sinuum, cum tabulis duplicibus Sinuum ejusdem," folio, Nuremberg, 1541. 

 All the writers who assert that sines of Regiomontanus were published be- 

 fore tiiose of Apian, go on the assumption that what is in the second edition 

 of the work on triangles is also in the first, which assumption is not true. 

 Lalande gives a wrong date, place and title, to this first edition. 



