Page:The Construction of the Wonderful Canon of Logarithms.djvu/61

CONSTRUCTION OF THE CANON. 37

HUS let the given sine be 7489557, of which the logarithm is required. The table sine nearest it is 7490786.6119. From this subtract the former with cyphers added thus, 7489557.0000, and there remains 1229.6119. This being multiplied by radius, divide by the easiest number, which may be either 7489557.0000 or 7490786.6119, or still better by something between them, such as 7490000, and by a most easy division there will be produced 1640.1. Since the given sine is less than the table sine, add this to the logarithm of the table sine, namely to 2889111.7, and there will result 2890751.8, which equals 2890751$$\scriptstyle \tfrac{4}{5}$$. But since the principal table admits neither fractions nor anything beyond the point, we put for it 2890752, which is the required logarithm.

ET the given sine be 7071068.0000. The table sine nearest it will be 7070084.4434. The difference of these is 983.5566. This being multiplied by radius, you most fitly divide the product by 7071000, which lies between the given and table sines, and there comes out 1390.9. Since the given sine exceeds the table sine, let this be subtracted from the logarithm of the table sine, namely from 3467125.4, which is given in the table, and there will remain 3465734.5. Wherefore 3465735 is assigned for the required logarithm of the given sine 7071068. Thus the liberty of choosing a divisor produces wonderful facility.

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