NAPIER COMMEMORATIVE LECTURE. 49 
it may please you who are inclined to these studies, to receive it 
from me and the translator, with as much good will as we recom- 
mend it unto you. Fare yee well.” 
To understand this work properly, we must remember 
that its chief object was to render easier computations 
involving the trigonometrical ratios. What we call the 
sine, cosine, etc., were by the mathematicians of Napier’s 
time regarded not as ratios but as lines. 
The line P M measured the sine of the are AP; OM 
was the cosine; AT the tangent, etc. In the tables, 
the values of the sine, cosine, tangent etc., were given as 
integers; for, as we have seen, the decimal notation for 
fractions had not been invented when they were compiled. 
If additional accuracy was required, they were computed 
on the assumption that the ‘* radius’’ was proportionally 
great. With Napier the radius or sinus totus was taken 
as 10’. Later, trigonometrical tables in which the radius 
was 10° were often used; and it is due to the use of these 
tables that the logarithmic sines, etc., as we sometimes 
call them, have the characteristics 10, 9, 8, etc. . 
As Napier takes the radius as 10’, and thus the sine of 
a right angle—the sinus totus—as 10’, it will now be clear 
why he works with the series :— 
D—May 21, 1914. 
