THE GENESIS OF LOGARITHMS 



By ALLAN FERGUSON, B.Sc. 

 Assistant Lecturer in Physics in the University College of North Wales 



In the historical development of mathematics the period covered 

 roughly by the seventeenth century must always, on two 

 counts, be held to be of primary importance, as this century 

 witnessed the birth of the fluxionary calculus and the discovery 

 of logarithms. It is proposed to deal with this latter discovery 

 in the present article. As the details of the discovery are of 

 remarkable interest to the mathematician, and as they are not 

 easily obtained and are couched in archaic language that is some- 

 what laborious reading, it seems that a restatement of the facts 

 may not be without interest and value. 



In order to make the survey fairly complete a preliminary 



discussion of the mathematical tables in use at the beginning 

 of the seventeenth century, together with a brief account of 

 the methods of computation adopted, will be given. 



Confusion of diction and thought will be avoided if it be 

 remembered that what we call the " trigonometrical ratios " 

 can be and were considered under two aspects — (i) that of 

 ratios, (2) that of lines. In (2), the older system, angles are 

 measured by the arc swept out by a revolving line whose 

 length must be the same for all angles. Then in the figure 

 the line BM measured the sine of the arc A B, O M (the sine 



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