Tt^ M. Biofs Abstract of Mr Napkr's 



Neither do we ever read now his other book, entitled, Mirifici 

 Logarithmorum Canonis construction which was only published 

 after his death, by his son, in 1619 ; a work in which Napier un- 

 folds, establishes, demonstrates, all the processes, all the me- 

 chanism of the construction of those logarithmic tables which he 

 did not choose in the first instance to unveil. We are now in- 

 dependent of his method, and of every thing except his primor- 

 dial idea. The immense development given to the algebraic 

 calculus by the use of literal symbols, the introduction of which 

 is due to Vieta, furnishes us, in the present day, with rapidly 

 and indefinitely converging series, by means of which we obtain 

 those same logarithms by a direct and immediate path, almost 

 without labour, and with a perfect adaptation of symbols, which 

 always enables us to see the present effect of those general oper- 

 ations which we express by formulae, and permits us to appreciate, 

 with a generalization not less perfect, the degree of approximation 

 of our results. Nevertheless, though the precision be boundless 

 with which these series may be pushed in search of logarithms, 

 I declare, to the honour of Napier, they effect nothing which 

 may not very easily be attained by his original method ; and if, 

 as is natural to suppose, this assertion appear somewhat rash to 

 our analysts, I hope immediately to prove it in a manner that 

 will remove every objection. 



But, in order to form a just idea of Napier''s labours, we must 

 study his own books (especially the second one, wherein he un- 

 folds his method), and not merely rely upon the abstracts that 

 have been given of them. Of all these abstracts the best, that 

 is to say the most concise and elaborate, is, in my opinion, that 

 which Hutton published to his Introduction to the Mathemati- 

 cal Tables of Sherwin, and which is reprinted, with that intro- 

 duction, in the first volume of Scriptores Logarithmici. Yet, 

 after all, this abstract is rather an exact reproduction of Napier's 

 steps, than any attempt to characterize them in their principle, 

 or appreciate them in their results, by a comparison with our 

 actual methods ; now, of all others, that is the very point of view 

 under which it is most delightful to contemplate an original in- 

 ventor. As for Montucla, the popular historian of mathema- 

 tics, one would almost be tempted to believe that he never had 

 in his hand Napier^s posthumous explanatory work, for he at- 



