P. HISTORY OF ' AATHEMATICAL - School of Mathematics

GEOMETRY
for similar. We have seen that '~eibnia' signs for congruence did not
use both lines occurring in the sign of equality = . Wolf was the first to
use explicitly - and = for congruence, but he did not combine the
two into one symbolism. That combination appears in texts of the
latter part of the eighteenth century. While the r was more involved,
since it contained one more line than the Leibnizian N, it had the
advantage of conveying more specifically the idea of congruence as
the superposition of the ideas expressed by and =. The sign -
for "similar" occurs in Camus' geometry,' for "similarJ' in A. R.
Mauduit's conic sections2 and in Karsten: - in BlassiBrels geometry:
s for congruence in Haseler's6 and Reinhold's ge~metries,~ - for
similar in Diderot's Encyclop6die,? and in Lorenz' ge~metry.~ In
Kliigel's W6rterbuchD one reads, "- with English and French authors
means difference"; '(with German authors - is the sign of similarity";
"Leibniz and Wolf have first used it." The signs - and s are used
by Mo1lweide;'O by Steinerl' and Koppef2 - is used by Prestel,I3
s by Spitz;14 - and 2 are found in Lorey's geometry,15 Kambly's
C. E. L. Camus, &?bmas de gh9rie (nouvelle Bd.; Paris, 1755).
A. R. Mauduit, op. cil. (The Hague, 1763), "Symbols."
W. J. G. Karaten, Leh~befif dm gesamlen Mathematik, 1. Theil (1767),
p. 348.
J. D. Blwih, Principes de ghmtrib 6hendaire (The Hague, 1787),
p. 16.
J. F. HiiBeler, op. cit. (Lemgo, 1777), p. 37.
0 C. L. Reinhold, Arithmetica Furensis, 1. Theil (Ossnabriick, 1785)' p. 361.
7 Diderot Encyclopddie ou Dietionnai~e ~ai.son4 des sciences (1781; 1st ed.,
1754), art. "Caractere" by D'Alembert. See also the Italian translation of the
mathematical part of Diderot's Encydo@die, the Dizwnario enciclopediw delle
ntalematiche (Padova, 1800), "Carattere."
8 J. F. Lorenz, Grundriss der Arithmetik zlnd Geometrie (Helmstiidt, 1798)' p. 9.
0 G. S. Kliigel, Mathemalisches Winterbuch, fortgesetzt von C. B. Mollweide,
J. A. Gmnert, 5. Theil (Leipzig, 1831), art. "Zeichen."
lo Carl B. Mollweide, Ezlklid's Elemenle (Halle, 1824).
11 Jacob Steiner, Geumetrische Constrtcclwnen (1833); Ostwald's Klass-iker, No.
60, p. 6.
* Karl Koppe, Planimdtrie (Essen, 1852)' p. 27.
U M. A. F. Prestel, Tabelarischer Grundriss dm EzperimataGphysik (Emden,
1856), No. 7.
14 Carl Spitz, Lehrbvch dm ebenen Geometrie (Leipzig und Heidelberg, 1862),
p. 41.
16 Adolf Lorey, Lehrbuch akr ebewn Geutnedrie (Gera und Leipzig, 18681,
p. 118.