Page:The Construction of the Wonderful Canon of Logarithms.djvu/82

58 REMARKS ON APPENDIX. As the quotients of the given are 3 and 7, their product is 21, which, multiplied by 84509804 the common divisor, makes 17.74705884 the  of the number produced.

It should be observed that the cube of the second number, and its equal the seventh power of the first (which some call secundus solidus), contain eighteen figures, wherefore its Logarithm has 17. ''in front, besides the figures following. The latter represent the Logarithm of the number denoted by the same digits, but of which 5, the first digit to the left, is alone integral, the remaining digits expressing a fraction added to the integer, thus $$\scriptstyle\frac{5854586408}{10000000000}$$ &c.has for its Logarithm 74705884. Again, of four places remain integral, 3. must be placed in front of the Logarithm, thus $$\scriptstyle 5585\frac{4586408}{10000000}$$ ''&c. has for its Logarithm 3.74705884.

Take some common divisor of the Logarithms, ''(the larger the better); divide each by it. Then let the first sine multiply itself and its products continuously until the number of these products is exceeded, by unity only, by the quotient of the second Logarithm; or until the power is produced of like name with the quotient of the second'' Logarithm. The same number would be produced if the second sine, which ts sought, were to multiply itself until it became the power of like name with the quotient of the first Logarithm, as is evident from the preceding proposition. Therefore