344
CONSTRUCTION OP
TRACT 25.
The 3d table consists of 69 columns, and each column of21 numbers or terms, which terms, in every column, are inthe continual proportion of 10000 to 9995, that is, nearly asthe first is to the last in the 2d table; and as 10000 exceeds9995 4*.y the 2Q00th part, the terms in every column will beconstructed by dividing each upper number by 2, removingthe figures of the quotient 3 places lower, and then subtract-ing them; and in this way it is proper to construct onlythe first column of 21 numbers, the last of which will be.9900473 - 5780 : but the 1st, 2d, 3d, &c, numbers, in all thecolumns, are in the continual proportion of 100 to 99, ornearly the proportion of the first to the last in the first co-lumn ; and therefore these will be found by removing thefigures of each preceding number two places lower, and sub-tracting them, for the like number in the next column. Aspecimen of this 3d table is as here below.
The Third Table.
Terms
1st Column.
2d Column.
3d Column.
&c till the 69th Col.
i
10000000.0000
9900000.0000
9801000.0000
8$c for
5048858.8900
2
9995000.0000
9895050.0000
9796099.5000
the 4th
5046334.4605
3
9990002.5000
9890102.4750
9791201.4503
5th, 6th,
5043811.2932
4
99S5007.4987
9885157.4237
9786305.8495
7th, &c
5041289.3879
A
9980014.9950
9880214.8451
9781412.6967
col. till
50387G8.7435
&c
&c till
&c
&c
the last
&c
21
9900473 5780
9801468.8423
9703454.1539
or
4998609.4034
Thus he had, in this 3d table, interposed between the radiusand its half, 68 numbers in the continual proportion of 100 to99 ; and interposed between every two of these, 20 numbersin the proportion of 10000 to 9995: and again, in the 2dtable, between 10000000 and 9995000, the two first of the 3dtable, he had 50 numbers in the proportion of 100000 to99999; and lastly, in the 1st table, between 10000000 and9999900, or the two first in the 2d table, 100 numbers in theproportion of 10000000 to 9999999 ; that is in all, about 1600proportionals; all found in the most simple manner, by little