P. HISTORY OF ' AATHEMATICAL - School of Mathematics

TRIGONOMETRY
147
A novel mark is adopted by Georg Vega,' he lets 45 V stand for 45 0
but occasionally uses the full circle or zero.
The weight of evidence at hand favors the conclusion that the
sign 0 for degree is the numeral zero used as an exponent in the theory
of sexagesimal fractions and that it is not the Greek letter omicron.
To prevent confusion- between circular measure and time measure,
both of which involve the words "minutes" and "seconds," and both
of which are used side by side by astronomers and navigators, it
became the common practice to mark minutes and seconds of arc by
, and ", and minutes and seconds of time by m and • (see also § 36).
515. Sign/or radians.-The word "radian" was first used in print
in 1873 by James Thomson, a brother of Lord Kelvin." It has been
quite customary among many authors to omit the word "radian"
in the use of circular measure and to write, for example, ;. or 11",
when; radians or 11" radians are meant. It has been proposed also to
use the Greek letter p and to write 2p, ~ 1I"p for two radians and threefifths
of 11" radians.' Others- have used the capital letter R in a raised
position, .as i
R
fori radians, or else the small letter" r as in l r for
one radian, or again the small r in parentheses' as in 2(r) for two
radians.
The expression "circular measure" of an angle has led to the suggestion
that radians be indicated by the small letter c, i.e., 2 c means
two radians.' However, "when the radian is the unit angle, it is customary
to use Greek letters to denote the number of radians, and the
symbol c is then often omitted. When capital English letters are
used, it is usually understood that the angle is measured in degrees.?"
1 Georg Vega, Vorlesungen uber Mathematik, Vol. II (Vienna, 1784), p. 5, 8.
16, 23, 27, 31, 185.
2 D. Andre, op. cit., p. 32.
3 Cajori, History of Mathematics (2d ed., 1919), p. 484.
4 G. B. Halsted, Mensuration (Boston, 1881), p. 83; T. U. Taylor and C. Puryear,
Plane and Spherical Trigonometry (Boston, 1902), p, 92.
6 A. G. Hall and F. G. Frink, Plane Trigonometry (New York, 1909), p. 73.
I G. N. Bauer and W. E. Brooke, Plane and Spherical Trigonmnetry (Boston,
1907), p. 7.
7 P. R. Rider and A. Davis, Plane Trigonmnetry (New York, 1923), p. 29.
• W. E. Paterson, Elementary Trigonmnetry (Oxford, 1911), p. 29.