P. HISTORY OF ' AATHEMATICAL - School of Mathematics

422 A HISTORY OF MATHEMATICAL NOTATIONS
I. Newton used dots and strokes for marking fluxions and fluents
(0% 567, 622). As will be seen, indices of various types occur repeatedly
in specialized notations of later date. For example, L. Euler'
used in 1748
xt xtt
d Y"
as co-ordinates of points of equal significance. Cotes2 used such strokes
in marking successive arithmetical differences. MongeS employed
strokes, K', K", K"', and also 'K', "K'.
378. The introduction of different kinds of type received inm
e d attention in the nineteenth ce2tury. Wolfgang Bolyai' used
Latin and Greek letters to signify quantities, and German letters to
signify points and lines. Thus, 3 signifies a line ab infinite on both
sides; ab" a line starting at the point a and infinite on the side b; Tib a
' line starting at b and infinite on the side a; a plane P extending to
infinity in all directions.
379. A remarkable symbolism, made up of capital letters, lines,
and dots, was devised by L. N. M. Carn~t.~ With him,
A, B, C, . . . . marked points
m, fi marked the segment AB and the circular arc AB
X?D
A3.m
xttt
Y"'
marked that the points B, C, D are collinear, C being
placed between B and D
is the point of intersection of the indefinite lines AB, CD
A- marked four points on a circular arc, in the order indicated
~2.6 is the point of intersection of the two arcs AB and CD
F KB'CD is the
--
straight line which passes through the points F
and AB'CD
1 L. Euler in Hislaire de llAcodemie r. d. scienees el d. bellea lettres, annee 1748
(Berlin, 1750), p. 175.
' Roger Cotes, Hannonia mensuramm (Cambridge, 1722), "Aestimatio errorum,"
p. 25.
G. Monge. Miscellanea Taurinensia (1770/73). See H. Wieleitner, Geschkhte
dm Mathematik, 11. Teil, 11. Hiilfte (1921), p. 51.
Wolfgangi Bolyai de Bolya, Tenlamen (2d ed.), Tom. I (Budapestini, 1897))
p. xi.
L. N. M. Camot, De lu Currlatwn dea $gures de gdomdtn'e (Paris, an IX=
1801), p. 40-43.