Full resolution (JPEG) - On this page / på denna sida - Logarithms
<< prev. page << föreg. sida << >> nästa sida >> next page >>
Below is the raw OCR text
from the above scanned image.
Do you see an error? Proofread the page now!
Här nedan syns maskintolkade texten från faksimilbilden ovan.
Ser du något fel? Korrekturläs sidan nu!
This page has never been proofread. / Denna sida har aldrig korrekturlästs.
^Logarithms.
Logarithms are a series of numbers computed in order to
facilitate all kinds of laborious calculations, such as evolution,
involution, multiplication and division.
Addition takes the place of multiplication, subtraction the
place of division; multiplication that of involution, and divi-
sion of evolution.
The logarithm of any given number is the exponent of the
power to which another fixed number, called the base, must be
raised in order to produce the given number.
There are two systems of logarithms in more or less general
use in mechanical calculations : namely, the Napierian system
and the Briggs system.
The Napierian system of logarithms was invented and
tables published by Baron John Napier, a Scotch mathema-
tician, in 1014, but these tables were improved by John Speidell
in 1619.
The modulus of any system of logarithms is a constant by
which the Napierian logarithm of any given number must be
multiplied in order to obtain the logarithm for the same number
in the other system.
The base of the Napierian system of logarithms is an in-
commensurable number expressed approximately by 2.718281828.
In mathematical works this base is usually denoted by the
letter e.
The Napierian logarithms are frequently called hyperbolic
logarithms, from their relation to certain areas included between
the equilateral hyperbola and its asymptotes.
The Napierian logarithms are sometimes called natural
logarithms.
The Briggs system of logarithms was first invented and
computed by Professor Henry Briggs of London in 1615, and
is usually termed the common system of logarithms. When-
ever logarithms in general is mentioned the Briggs system is
always the one referred to.
The Briggs system of logarithms has for its modulus
0.4342945, and 10 for its base. Therefore the Briggs logarithm
of a number is the exponent of the power to which 10 must be
raised in order to give the number. Thus
:
(7i)
<< prev. page << föreg. sida << >> nästa sida >> next page >>
