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And the co-tangent is equal to the fquare of radius 
divided by the tangent. 
Now the radius being unity, its fquare is alfo unity. 
Therefore the tangent and co-tangent of any arc 
are the reciprocals one of the other. 
But the reciprocals of numbers are correlatives to 
the arithmetical complements of their logarithms. 
Therefore the logarithms of a tangent and its co- 
tangent are arithmetical complements one of the 
other; and confequently will fall at equal diftances 
from 45 degrees. 
Therefore, in the line of logarithmic tangents, the 
divifions to degrees under 45 ferve alfo for thofe 
above ; both being equally diftant from 4^ degrees* 
To conftruft the line of logarithmic verfed fines. 
As the greatefi: number of degrees will fall within 
the limits of the fcale by beginning at i8o Q ; there- 
fore the termination of this line is at 180 0 , which is 
put againft 9 o° on the fines : and altho' the numbers 
annexed to the divifions increafe in the order from 
right to left, yet they are only the fupplements of the 
verfed fines themfelves. 
Now fubtradt the logarithmic verfed fines of fuch 
degrees and parts of degrees as are intended to be put 
on the fcale, from the logarithm verfed fine of 180°; 
then the remainders taken from the forefaid fcale of 
equal parts, and laid fuccefiively from the termination 
of this line, will give the feveral divifions fought. 
The following table to every 10 degrees was con- 
ftrudted in the foregoing manner, and are the numbers 
to 
