Elementary arithmetic, with brief notices of its history... by Robert Potts.

12
of the modulus for transforming Napier's logarithms to logarithns whose
Iasle is 10.1
The modulus M-lo 1 -log,10
and log 10 = log,(2 x 5) — log,2 + log,5.
*KT 0 0 ~ - C \ 1
Now logu =logv + 2 { + -
n u + v 3'\ + VI 5vu + v
Let = 2, = 1,
The calculation of loge2 and log,5 may be thus exhibited:1og,2 =2 - +. +3- 3. + &c.
-= '33333333
1 0370337...... 012345678
3 93 3 3 3
1 11 11_
- 1.; - 0041152... '000...... 823045
3S 9 3a 5 34
1=.1 1 000-457247... - 000065321
37 9 35 7 37
1 _ 1 1 - 000050805..... 1 000005645
9 37 9 30
11 _ -64 1
_U= l.I = -00000545 - '000000513
311 9 3 11 311
L 1 000027 '000000048:33 9 311 13 31".
1 __ 1 00000.1 0000001
L L- 000000069..'000000004
31S 9 313 15 315
000000007 00000000
3 '= 93 -' 17 317..~~
'346573587
2
loge 2 = 693147174
log 5 = og, 4 + 2.9.-&c.
- = -111111111
9
1 - x '012345678 = '001371742..... 1 - 000457247
9:9.3 9a.- = Ix '000152415 = -000016935...... 000003387.) 9 5 9.'
L 1 x.000001881 = 00002C = 000000029
97 9 7 70
'111571772
2
*223143544
log, 4 = 2 log, 2 = 1-386294348.. log, 5 = 1'609437892
LogJ3 = 2-302585,092994,045684,017991,... to twenty-four places of decimals.