Mr. hellins’s Theorems 
312 
The odd powers of £ divided I 5 y their 
refpedtive indices. 
I ft, 0*14285714286 
3d, 0*00097181730 
5th, 0*00001189980 
7th, 0*00000017347 
9 th, 0*00000000275 
lith, 0*00000000004 
The fum, 0*14384103622 is f 1 . of f. 
4 
o* 575364 i 488 twice 1. f . 
The odd powers of T x r divided by their 
refpe&ive indices. 
ift, 0*05882352941 
3d, 0*00006784721 
5th, 0*00000014086 
7th, 0*00000000035 
Thefura, 0*05889151783 is 1 1 . off, 
2 
Log. f, 0*11778303566 
2 log. f, 0*57536414488 
Log. of 2. 0*69314718054 
But it is obvious, that this operation gives not only 
the logarithm of 2 but that of 3 alfo : for the logarithm 
of 4 being given from that of 2, and the logarithm of | 
computed above, the logarithm of 3 is had, being = log. 
of 4 - log. of f . 
Log. of 4 1*38629436108 
Log. of 4 0*28768207244 
Log. of 3 1*09861228864 
Other examples of the ufe of thefe theorems in Jhewing how 
eafily the logarithms of great fractions are derived from 
thofe of fmall ones. 
If the logarithm of || were given, or computed, we 
mav very eafily find the logarithm of |4 : for (by the- 
2 orem 
