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

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log,122714=4-3562936; construct such a table for calculating the
logarithms of numbers between 227130 and 227140.
3. If logo167833=4-8314410, and log,,67832 =48314346; find
log,067832800.
4. Given loglo71820 - 4-8562454, and log1o71821 = 4-8562514;
find logi'007182035.
5. Having given logo033819 = 4-5291608, and
loglo33818 = 4-5291479; find the logarithm of 338-185.
6. Having given logo71968=4'8571394; diff. for 1=60: find
the value of log,1o(0719686)1 to seven places of decimals.
7. Find the numerical value of log1o(-242447)'4, having given
log,024214 =4-3846043; diff. for 1 = 179.
XXIV.
1. The difference of successive integral numbers being invariable,
shew that as those numbers increase, the difference of their logarithms diminishes: also that the difference of the logarithms of two
consecutive numbers n and n + 1 is less than - in the Napierian
n
system, and less than 1 in the common system.
2Ma
2. Shew how to find the number corresponding to a given logarithm when it is not found exactly in the tables.
Given log-,,7G49 = 4-5757534, and log837650 =4-5757650; find
the number corresponding to the logarithm 1-575638.
3. Given logo,l 0686= 02881517, and logl01l0687= '02885581;
find the number of which the logarithm is -02883549.
4. If log0o4-3125=- 6347291, and logo4-3126= '6347392; determine the number whose logarithm is 3-6347362.
5. Given that e is 2-7182818, and that logo027182= 43428147
and log,o27183 =4:342974; find log,0999995 correctly to twelve
places.
6. Approximate to the value of 5'), having given logo1 2 = -30103,
logo0349485=5.543428, log,1l 562944= -193943, log3-655 = 562887,
log1r,3856 = 563006.
7.. Find the value of l10 3, having given log1021544 = 4-33032-3
lo10;21545 = 43333465, logOl4270= 4 1544240, log,,l14271 = = 15 1
8. Given 93 = 1000, log,12 = -30103, log10300 = 2-4771213,
logl,'47712 = 1-6786276, log-47713 = 1'6786367; shew that the
value of x lies between 11- and 14.
9. Could the results of calculation be depended on, which are made
by a system of logarithms where the value of the base cannot be
exactly determined?
10. Was Napier led to the discovery of logarithms by geometrical
or numerical considerations? Explain his method, and compare it
with the method by which Newton was led to the discovery of fluxions.