The construction of the wonderful canon of logarithms

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Page 76
SOME
NOTES
BV THE LEARNED
HENRY
BRIGGS
ON THE FOREGOING PROPOSITIONS.
[a] ^;;^^ Iven an arc, to find the logarithm of its versed
sine.
—
To the end of this proposition \* / should like to add
the following
Conversely, given the logarithm of a versed sine, to find
its arc.
Add the known logarithm of the required versed sine to the logarithm
of 2,0°, viz., 6gsi47, and half the sum will be the logarithm
of half the arc sought for.
Thus let 35791 be the given logarithm of an unknown
versed sine, whose arc is also unknown.
To this logarithm add 693147, and the sum will be
728938, half of which, 364469, is the logarithm of
43° 59' 12)' • The arc of the given logarithm is therefore
87° 59' 6", and its versed sine is 9648389.
Again, let a negative logarithm, say —54321, be the
known logarithm of the required versed sine. To this
logarithm