P. HISTORY OF ' AATHEMATICAL - School of Mathematics

208 A HISTORY OF MATHEMATICAL NOTATIONS
It should be noticed that the 1797 edition of Lagrange's Theme des
jonctions is not the first occurrence of the accent as the mark for
derivatives. In 1770 '1"
occurs for ~: in his Nouvelle methode pour
rtsoudre les equations liuerales, and in 1759 the notation is found in a
part of a memoir by Francois Daviet de Foncenex in the Miscellanea
Taurinensia, believed to have been written for Foncenex by Lagrange
himselLI
576. J. Pasquich.-Another writer who at this time attempted a
reform of the calculus was Johann Pasquich, of Ofen (Budapest) in
Hungary, in a paper entitled "Exponential Rechnung."! Postulating
that every function can be expressed in the form y=Axa+Bx b+ .... ,
he calls the function ey=aAxa+bBx b+ .... the exponential of y;
"ty" is really the limit of x6y .
6x
J. P. Grilson.-A change similar to that of Pasquich was suggested
by Johann Philipp Gruson, 'ofBerlin, in his "Calcul d'exposition.:" He
reaches the same limit which had been used by Pasquich. Gruson
indicated it by an inverted and rounded E; thus 3F represented the
limit of X6F. This notation is mentioned by S. F. Lacroix in his
6x
Traite du Calcul dijJerentiel et du Calcul integral.
The notations of Pasquich and Gruson found no acceptance among
the mathematicians of their time and have not been drawn upon since
for the designation originally assigned. The notation of Lagrange, on
the other hand, was adopted by many and has been found a useful
adjunct of other calculus notations.
577. L. F. A. Arbogast.-Still another symbolism, which has been
extensively used in recent years, was made public by L. F. A. Arbogast
in his De Calcul des Derivations (Strasbourg, 1800). This new
calculus was offered as comprising the theory of series, and included
the differential calculus as a special case. An outline of it was presented
in the form of a memoir in 1789 to the Academy of Sciences at
Paris, but was not published at the time. It was mentioned in the
1 P. E. B. Jourdain in Proceed. 5th Internat. Congress (Cambridge, 1913), Vol.
II, p. 540.
: J. Pasquich, "Anfangsgriinde einer neuen Exponentialrechnung," Archiv
der reinen und angew. Math., Vol. II (1798), p. 38S-424. Our information is drawn
from M. Cantor, op., cit. Vol. IV, p. 667, 668.
. 3 J. P. Griison, "Le Caleul d'exposition," Mem. acad8mie (Berlin, 1798),
Pub. 1801, p. 151-216; (1799 and 1800) Pub. 1803, p. 157-88.