314 Mr. hellins’s 'theorems 
But when the numerator of the fraffion, whofe loga- 
rithm is given, is odd, theorem 2. is more commodious. 
For taking | , as before, we have 2 log. | — log. || = log. 
where the fraction to be involved is Again, 
2 log. | - log. || = log. I, where the fradtion is And 
a log. | - log. | = log. I, where we have only to take the 
difference of logarithms, as the logarithm of | as well as 
that of | is given. 
All the above calculations are of hyperbolic loga- 
rithms; but the fame theorems hold good for Mr. 
briggs’s, or any other. I will give an example in the 
computation of briggs’s logarithm of 7 from others 
already known. 
Let the logarithms of 100, 99, and 50, be given; 
then (by theorem 1.) 2 log. — + -Ej — = log. f|, or 
v & 99 99!’-- 1 6 49 
log- + k lo g- = * Io s- « ’ and then t lo s- 5 ° 
-t log- If = r lo g- 49 = lo g- 7 - 
Log. of ^ - 0*00436480540245 
^ lo S- of f ( = ^01 ~ = ) 0-00002215675128 
flog, of If “ 0-00438696215373 
| log. of 50 0-84948500216801 
Log. of 7 - *> 0-84509804001428 
SCHOLIUM. 
