162 Memoir of John Napier, 



he could derive little assistance from the writings of ma- 

 thematicians, and even from those who have written par- 

 ticularly on the history of the mathematics ; for, hy a fatality 

 almost inevitably attached to inventors whose discoveries 

 are subsequently improved by the succeeding progress which 

 they excite, the original work of Napier entitled, " Mirifici 

 Logarithmorum Canonis Description published in 1614, is 

 never read, although he explains in it the mode of generation 

 which he attributed to the new quantities called by him 

 artificial numbers, or logarithms, to which he joins their 

 numerical properties, exhibiting their use in simplifying 

 arithmetical calculations, when it is necessary to multiply 

 numbers by each other, or to divide the one by the other, 

 as well as their employment in the determinations of trigo- 

 nometry and astronomy, and, lastly, the numerical tables 

 containing the logarithms of trigonometrical lines called 

 sines, co-sines, tangents, and secants, calculated from minute 

 to minute for every degree on the quarter of the circle, 

 which, without the employment of the invention would cost 

 enormous labour. All this is given without any explanation, 

 without any insight into the ideas which had led him to 

 conceive the admirable utility of these tables, nor upon the 

 means which he employed in calculating them. His work 

 entitled, "Mirifici Logarith?no7-umCanonisConstructio" is also 

 no longer read. It was published after his death, by his 

 son, in 1619. In it he explains and demonstrates all the 

 processes, all the mechanism in the construction of his 

 logarithmic tables, which he did not wish to develope at 

 first. We do not require at the present day a knowledge 

 of his original ideas, nor of his method. The immense 

 developement given to algebraic calculation, by the xise of 

 letters as symbols, of which, the introduction is due to Vieta, 

 has furnished us with rapidly, indefinitely, converging 

 series, by means of which, we attain the same logarithms in, 

 a direct way, almost without labour, with a neatness of sym- 

 bols which permits us always to see the present effect of 

 general operations which we express by formulae, and 

 enables us to appreciate the degree of the approximation of 

 our results. Although the precision to which they may be 

 pushed is without limit, still it must be asserted to the 

 honour of Napier, that the same advantage is connected 



