Page:The Construction of the Wonderful Canon of Logarithms.djvu/40

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16 CONSTRUCTION OF THE CANON.

Third Column.
9801000.0000
9796099.5000
9791201.4503
9786305.8495
9781412.6967
&c
descending
to
9703454.1539

Thence 4th, 5th
&c., up to
&c., up to
&c., up to
&c., up to
&c., up to
&c., up to
finally to

69th Column.
5048858.8900
5046334.4605
5043811.2932
5041289.3879
5038768.7435
&c
descending
to
4998609.4034

21.Thus, in the Third table, between radius and half radius, you have sixty-eight numbers interpolated, in the proportion of 100 to 99, and between each two of these you have one numbers interpolated in the proportion of 10000 to 9995; and again, in the Second table, between the be two of these, namely between 10000000 an 9995000, you have fifty numbers interpolated in the proportion of 100000 to 99999; and finally, in the First table, between the latter, you have a hundred numbers interpolated in the proportion of radius or 10000000 to 9999999; and since the difference of these is never more than unity, there is no need to divide it more minutely by interpolating means, whence these three tables, after they have been completed will suffice for computing a Logarithmic table.
21.Hitherto we have explained how we may most easily place in tables sines or natural numbers progressing im geometrical proportion.
22.It remains, in the Third table at least, to place beside the sines or natural numbers decreasing geometrically
their