Page:The Construction of the Wonderful Canon of Logarithms.djvu/70

46 CONSTRUCTION OF THE CANON.

INCE ''the logarithms found by 54 sometimes differ from those found by 58 (for example, the logarithm of the sine 378064 ts 32752756 by the former, while by the latter it 1s 32752741), it would seem that the table of sines is in some places faulty. Wherefore I advise the learned, who perchance may have plenty of pupils and computors, to publish a table of sines more reliable and with larger numbers, tn which radius is made 100000000, that is with eight cyphers after the unit instead of seven only. Then, let the First table, like ours, contain a hundred numbers progressing in the proportion of the new radius to the a less than it by unity, namely of 100000000 to 99999999.''

Let The Second table also contain a hundred numbers in the proportion of this new radius to the number less than it by a hundred, namely of 100000000 to 99999900.

Let the Third table, also called the Radical table, contain thirty-five columns with a hundred numbers in each column, and let the hundred numbers in each column progress in the proportion of ten thousand to the number less than it by unity, namely of 100000000 to 99990000.

Let the thirty-five proportamals standing first in all the columns, or occupying the second, third, or other rank, progress among themselves in the proportion of 100 to 99, or of the new radius 100000000 to 99000000.

In continuing these proportionals and finding their logarithms, let the other rules we have laid down be observed. From