Page:The Construction of the Wonderful Canon of Logarithms.djvu/58

34 CONSTRUCTION OF THE CANON.

pute, at one time, all the logarithms of the same rank, namely all the second logarithms in each of the columns, then all the third, then the fourth, and so the others, by continuously adding 100503.3210291 to the logarithm in one column, that the logarithm of the same rank in the next column be brought out. For by either method may be had the logarithms of all the proportionals in this table; the last of which is 6934250.8007528, corresponding to the sine 4998609.4034.

47.In the Third table, beside the natural numbers, are to be written their logarithms; so that the Third table, which after this we shall always call the Radical table, may be made complete and perfect.

This writing up of the table is to be done by arranging the columns in the number and order described (in 20 and 21), and by dividing each into two sections, the first of which should contain the geometrical proportionals we call sines and natural numbers, the second their logarithms progressing arithmetically by equal intervals.

The Radical Table.

First column.
Natural numbers	Logarithms.
10000000.0000	.0
9995000.0000	5001.2
9990002.5000	10002.5
9985007.4987	15003.7
9980014.9950	20005.0
&c., up to	up to
9900473.5780	100025.0

Second column.
Natural numbers	Logarithms.
9900000.0000	100503.3
9895050.0000	105504.6
9890102.4750	110505.8
9885157.4237	115507.1
9880214.8451	120508.3
up to	up to
9880214.8451	120508.3

and