P. HISTORY OF ' AATHEMATICAL - School of Mathematics

LOGARITHMS
113
en general,
aNsera la n-ieme puissance de l'ordre N de a."
The need of the novel symbolism suggested by Burja was not recognized
by mathematicians in general. His signs were not used except
by F. Murhard! of G6ttingen who refers to them in 1798. By the
sign "log i" Robert Grassmann? marked the quantity e which yields
the relation be = a. The Germans considered several other notations.
In the relation 2 3=8, Rothe in 1811 and Martin Ohm" in 1823 suggested
"8?2=3," while Bischoff in 1853 wrote I\.... for "log," and
K6pp6 in 1860 proposed /if = 3. Kopp's sign is favored by Draenert.
F. J. Studnicka- of Prague opposes it as hasslieh and favors the use
of "1" for a natural logarithm, and e; (derived, as he says, from "log,"
"lg," e,) for Briggian logarithms, and "e" ~" for logarithms to any
base e as the equivalent of Sch16milch's "loge b." E. Bardey opposes
the introduction of any new logarithmic symbol. Paugger" simply
inverts the radical sign V, and writes Vp=a andj~p=m (identical
with log, p=m). Later on in his Operationslehre (p. 81) Paugger
uses a modification of the Greek letter A, as shown in am=b, Vb=a,
~b=m. The editor of the Zeitsehrift, J. C. V. Hoffmann," prefers in
the case an= p, the symbolisms n = Ii(, and for antilogarithm
,~=p. J. Worpitzky and W. Erler! propose a modified l, namely,
2., so that log (be) to the base a would be written :J..."
a
Landen'? marked by log (RQ': PQ')the hyperbolic logarithm Of~~: ,
or the measure of the ratio of RQ' to PQ.
1 Friederich Murhard, System der Elemente der allgemeinen Grossenlehre
(Lemgo, 1798), p. 260.
2 Robert Grassmann, Zahlenlehre oder Arithmetik (Stettin, 1872), p. 45.
3 See Draenert in Zeitschr.j. math. u. naturwiss. Unterricht, Vol. VIII (Leipzig,
1877), p. 266.
t Anton Bischoff, Lehrbuch der Algebra (Regensburg, 1853), p. 265.
6 Kopp, A usfuhrung gewlJhnlicher ZijJerrechnungen mittelst Logarithrrum
(Osterprogramm des Realgymnasiums zu Eisenach, 1860); also in his Triqonometrie
(1863) and Arithmetik (1864).
8 Zeitschr. f. math. u. naturw. Unterricht, Vol. VIII (1877), p. 403.
70p. cit., Vol. VIII,p. 268, 269.
80p. cit., Vol. VIII, p. 270. I Op.cit., Vol. VIII, p. 404.
10 John Landen, Mathematical Lucubratio1I8 (London, 1755), Sec. III, p, 93.