Page:The Construction of the Wonderful Canon of Logarithms.djvu/76

52 APPENDIX.

A saving of half the Table of Loga-
rithms.

OF two ares making up a quadrant, as the sine of the greater ts to the sine of double its arc, so ts the sine of 30 degrees to the sine of the less. Whence the Logarithm of the double arc being added to the Logarithm of 30 degrees, and the Logarithm of the greater being subtracted from the sum, there remains the Logarithm of the less.

The relations of Logarithm &
their natural numbers
to each other.

[A] 1.L Et two sines and their Logarithms be given. If as many numbers equal to the less sine be multiplied together as there are units in the Logarithm of the 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 the product of the two Logarithms.

2.As the greater sine ts to the less, so ts 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