P. HISTORY OF ' AATHEMATICAL - School of Mathematics

382 A HISTORY OF MATHEMATICAL NOTATIONS
Descartes; these writers have endeavored to connect this s with older
symbols or with Arabic words. Thus, J. Tropfkell P. Treutlein,2 and
M. CurtzeS advanced the view that the symbol for the unknown used
by early German writers, 2 , looked so much like an s that it could
easily have been taken as such, and that Descartes actually did interpret
and use it as an s. But Descartes' mode of introducing the
knowns a, b, c, etc., and the unknowns z, y, x makes this hypothesis
improbable. Moreover, G. Enestrom has shown4 that in a letter of
March 26, 1619, addressed to Isaac Beeckman, Descartes used the
symbol 2 as a symbol in form distinct from x, hence later could not
have mistaken it for an 2. At one time, before 1637, Descartes5 used
z along the side of 2; at that time x, y, z are still used by him as
symbols for known quantities. German symbols, including the 2 for
s, as they are found in the algebra of Clavius, occur regularly in a
manuscript6 due to Descartes, the Opuscules de 1619-1621.
All these facts caused Tropfke in 1921 to abandon his old view1 on
the origin of x, but he now argues with force that the resemblance of
z and 2, and Descartes' familiarity with 2, may account for the
fact that in the latter part of Descartes' GdomBtrie the x occurs more
frequently than z and y. Enestrom, on the other hand, inclines to
the view that the predominance of z over y and z is due to typographical
reasons, type for s being more plentiful because of the more
frequent occurrence of the letter x, to y and z, in the French and Latin
language^.^
There is nothing to support the hypothesis on the origin of x
due to Wertheim? namely, that the Cartesian x is simply the notation
of the Italian Cataldi who represented the first power of the
unknown by a crossed "one," thus Z. Nor is there historical evidence
1 J. Tropfke, Geschiehle der Elementar-Malhematik, Vol. I (Leipzig, 1902), p.
150.
S P. Treutlein, "Die deutsche COBB," Abhndl. z. Geechiehle d. mathemutish
Wi8S., V0l. 11 (1879), p. 32.
8 M. Curtze, ibid., Vol. XI11 (1902), p. 473.
4 G. Enestrom, Biblwtheaa mdhemdiea (3d ser.), Vol. VI (1905), p. 316, 317,
405, 406. See also his remarks in ibid. (1884) (Sp. 43); ibid. (1889), p. 91. The
letter to Beeckman is reproduced in Q3wl.e~ de Descartes, Vol. X (1908), p. 155.
6 (Ewes de Descurtes, Vol. X (Paris, 1908), p. 299. See also Vol. 111, Appendix
11, No. 48g.
Ibid., Vol. X (1908), p. 234.
J. Tropfke, op. cil., Vol. I1 (2d ed., 1921), p. 44-46.
8 G. Enestrom, Biblwtheca mdhemotiea (3d ser.), Vol. VI, p. 317.
G. Enestrom, ibid.