The construction of the wonderful canon of logarithms

, A
52 Appendix.
saving of half the Table of Loga-
RITHMS.
OF two arcs making up u quadrant, as the sine of the
greater is to the sine of double its arc, so is the sine
of 30 degrees to the sine of the less. Whence the Logarithm
of the double arc being added to the Logarithm of 2,0
degrees, and the Logarithm of the greater being subtracted
front the sum, there remains the Logarithm of the less.
The relations
of Logarithms &
their natural numbers
to
each other.
[A] I. T Et two sines and their Logarithms be given. If as
J— ' many numbers equal to the less sine be multiplied
together as there are units in the Logarithm ofthe greater;
and on the other hand, as many numbers equal to the
greater sine be multiplied together as there are units in
the Logarithm of the less ; two equal numbers will be produced,
and the Logarithm of the sine so produced will be
theproduct of the two Logarithms.
2. As the greater sine is to the less, so is the velocity of
increase or decrease of the Logarithms at the less, to the
velocity of increase or decrease of the Logarithms at the
greater.
3. Two sines in duplicate, triplicate, quadruplicate, or
other ratio, have their Logarithms in double, triple, quadruple,
or other ratio.
4. And two sines in the ratio of one order to another order,
as for instance the triplicate to the quintuplicate, or the
cube