P. HISTORY OF ' AATHEMATICAL - School of Mathematics

322 A HISTORY OF MATHEJ\lATICAL NOTATIONS
designates the projection upon the horizontal and vertical planes of a
point 0 by Oh and 0'. Aubre marks the four right dihedral angles
formed by the interesting horizontal and vertical planes by A,S, P,S,
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P,I, A,I, where A stands for anierieur, S for sup~rieur, P for posierieur,
I for inferieur. A straight line in space is marked by capital letter,
say D, and its projections by Dh and D". Church' denoted a point in
space by, say, M; its horizontal projection by m; and its vertical by
m'; a line by, say, MN. Wiener represents points by Latin capitals,
surfaces by black-faced Latin capitals, lines by small Latin letters,
angles by small Greek letters. Berthold! marks a point by, say, a;
its horizontal projection by a'; and its vertical by a". He marks a
line by, say, abo Bernhard! prefers small Latin letters for points,
Latin capitals for straight lines and surfaces, small Greek letters for
angles. He uses X for intersection, so that a=GXL means that the
point a is the intersection of the coplanar lines G and L; PI and P 2
are the two mutually perpendicular planes of projection; X the axis of
projection; a' and a" are the projections of the point a, G' and Gil of
the line G; 01 and g2 are the traces of G; E 1 and E 2 are the traces of the
plane E.
Different again is the procedure of Blessing and Darling." With
them, planes are represented by capital letters, the last letters of the
alphabet being used, thus, P, Q, R, S, T, U; the horizontal trace of a
plane has the letter H prefixed, as in HP, HQ, etc.; the vertical trace
has the letter V prefixed, as in VP, VQ, etc. The ground line is
marked G-L; a line in space C-Dhas two projections, c-d and
c' -d'.
The illustrations cited suffice to show the lack of uniformity
in notation." They indicate, moreover, that the later books on descriptive
geometry introduce a larger amount of symbolism than
did the earlier.
1 Albert Church, Elements oj Descriptive Geometry (New York, 1870), p. 2, 5.
2 Christian Wiener, Lehrbuch de:r Darstellenden Geometrie, Vol. I (Leipzig,
1884), p. 62.
s Die DarsteU~ Geometric, von W. H. Behse, bearbeitet von P. Berthold,
1. Theil (Leipzig, 1895), p. 3, 11.
• Max Bernhard, Darstellende Geomeirie (Stuttgart, 1909), p. 3.
AGeorge F. Blessing and Lewis A. Darling, Elements oj Descriptive Geometry
(New York, 1913), p. 19, 20, 49.
6 Consult also G. Loria, "I doveri dei simboli matematici," Bollettino deUa
Mathesis (Pavia, 1916), p, 35.
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