164 Memoir of John Napier, 



speaks in his introduction to the Rudolphine tables, as 

 having thought of something of the same kind, without 

 publishing it.* But what is the use of discussing preten- 

 sions which have not been produced, and which no one at 

 present can see or appreciate 1 



At the time when Napier invented the logarithms, all 

 mathematicians, all astronomers, and they were then very 

 numerous, felt the want of some method which would sim- 

 plify the prodigious calculations which were necessary for 

 the resolution of the celestial triangles, the only application 

 of mathematics which was then known. Different scientific 

 details attest the trials made in this respect by Byrge, as 

 well undoubtedly as by many others, among whom Kepler 

 himself may be mentioned ; and, in short, when we think 

 of what must be the numerical calculation of the tables of 

 natural sines and tangents, for a radius expressed by a mil- 

 lion, or even by ten millions of parts as they were then con- 

 structed ; when we consider that all this required constant 

 divisions and multiplications which were required to be 

 accurately made, without omitting a single cypher from 

 the largest numbers, we can easily understand that the 

 desires of mathematicians would be directed to the object 

 of freeing themselves from such drudgery, and, that neces- 

 sity would suggest numerous methods for attaining this 

 desirable end. To these titles his right of inventor, but of 

 inventor only, is incontestible. But this right becomes, if 

 possible, more clear still, when we study the principle of 

 his tables, when we expose their basis, when we understand 

 the originality, and appreciate the justice with which he 

 applies it, and the precision of the results which he deduces. 

 If I can restore what commentators have consigned to ob- 

 livion, I may say what Cicero says of Archimedes : " Humi- 

 lem homunculum e radio et pulvere excitabo." But I shall 

 then have given subject of satisfaction to philosophers who 

 love the glory of their predecessors as their heritage, and 

 are happy when justice is rendered to their works. 



It was the great genius of Syracuse, in his treatise " De 



* The words are " Qui tamen apices logistici Justo Byrgio niultis annis ante 

 editionem neperianam viam pranverunt ad ipsos logarithmos. JEtsi homo cunctator 

 et aecretorum suorum eustos foetum in parhi destituit, non ad usus publicos 

 educavit. — (Tab. Rud. iii. p. 11 in fol. ) 



