524 Prof. De Morgan on the almost total DisapiJearance 



first half, and so on. But the very reverse is the fact; the 

 names cosine, cotangent and cosecant, are the consequence, 

 not the cause, of this duplicate system of arguments. Rheticus 

 made his arrangement with a view to separate from each other 

 all the cases in which the greater side and the less side were 

 data. This involved the bringing into the same line the tan- 

 gent of each angle with the tangent of its complement, and 

 the same for the secant. Completeness then required that 

 the same should be done with the sine. The introduction of 

 the terms sine of the complement, complemental sine, and 

 cosine, &c., followed after an interval of more than half a cen- 

 tury, and was a consequence of the semi-quadrantal arrange- 

 ment. 



The dialogue at the end is between Philomathes, a supposed 

 friend of Rheticus, and Hospes, his pupil. The pupil asks 

 what the intention of the book is, and is answered at length. 

 He suggests that, perhaps, the intention may be to complete 

 the system of Copernicus, by publishing tables from it resem- 

 bling those then in use. But he is answered, that Rheticus 

 would rather that Copernicus himself had not done so much 

 in this line, as he thereby diminished the geometrical practice 

 of the learner. The modern astronomer, if such a one there 

 be, whose luxurious means render him discontented whenever 

 he has to go to the common trigonometrical tables, even of 

 logarithms, should think of Rheticus, so well content with his 

 intervals of ten minutes, and their differences, that he asked 

 for nothing more, and regretted that any further help should 

 be interposed between the observer and his wholesome exer- 

 cise. I think I might have hoped for his sanction to an opi- 

 nion which has been for a long time my own, namely, that the 

 only way of learning to use a table thoroughly well, is to learn 

 to do without it. 



There is much examination yet wanted into the history of 

 the sixteenth century. The era of logarithms, of literal alge- 

 bra, and of sound mechanics, has naturally diverted attention 

 from the day of smaller things. One question has never been 

 properly considered : what were the immediate producing 

 causes of that burst of successful energy which marks the first 

 half of the seventeenth century ? 



The biography of Rheticus may be collected from the pre- 

 face to the OjMS Palatinum, Teissier's Eloges des Savaiis, with 

 the references therein given, &c. He led a wandering life for 

 a calculator of such a mass of tables, being successively with 

 Copernicus at Wittemberg, at Leipsic, and in Hungary. 

 And his friend and correspondent, Peter Ramus, informs us 

 {Schol. Mathem.), that he taught at Cracow, and would have 



