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

14

LOGARITHMIS.

death before series were employed. The series for log. (1 + x) was first
invented by Mlercator, in 1667, and published in his "Logarithmotechnica." James Gregory, in his "Exercitationes Geometricac,"
proved the series for log. (1 + x), log. (1 -x), and log. (1 + x)-log. (l —x).
Dr. Edmund Halley, in a paper printed in the "Transactions of the
Royal Society for 1595," showed how to find the logarithms of numbers,
and to solve the converse problem by a process of algebra. This
paper ends with these words:-" Thus I hope I have cleared up the
doctrine of logarithms, and shown their construction and use independent
from the hyperbola, whose affections have hitherto been made use of
for this purpose, though this be a matter purely arithmetical, nor
properly demonstrable from the principles of geometry. Nor have I
been obliged to have recourse to the method of indivisibles, or the
arithmetic of infinites, the whole being no other than an easy
corollary to Mr. [Sir Isaac] Newton's ' General Theorem' for forming
roots and powers."
Euler, in his "Introductio in Analysin Infinitorum," has exhibited
the properties of logarithms and the series for the construction of tables
nearly in the form in which they are employed by mathematicians at
the present time.
For the details of the history and the various methods and improvements, the student is referred to the works of the original authors,
which he will find noted in the "Scriptores Logarithmici " of Baron
Maseres, and in the introduction prefixed to the "Tables of Logarithms " published by Dr. HIutton.