38 CONSTRUCTION OF THE CANON.
For since the ratio of every sine to its half is the same as that of radius to 5000000, therefore (by 36) the difference of the logarithms of any sine and of its half is the same as the difference of the logarithms of radius and of its half 5000000. But (by 34) the difference of the logarithms of radius and of the sine 5000000 is the same as the logarithm itself of the sine 5000000, and this logarithm (by 50) will be 6931469.22. Therefore, also, 6931469.22 will be the difference of all logarithms whose sines are in the proportion of two to one. Consequently the double of it, namely 13862938.44, will be the difference of all logarithms whose sines are in the ratio of four to one; and the triple of it, namely 20794407.66, will be the difference of all logarithms whose sines are in the ratio of eight to one.
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