P. HISTORY OF ' AATHEMATICAL - School of Mathematics

GEOMETRY 403
Opuscula mthematica hactenus inedita (1677), a posthumous work
(8 184).
Kliigell mentions a cube a as a symbol attached to cubic meas-
ure, corresponding to the use of
in square measure.
Euclid in his Elements uses lines as symbols for magnitudes, including
numbers,' a symbolism which imposed great limitations upon
arithmetic, for he does not add lines to squares, nor does he divide a
line by another line.
360. Signs for angles.-We have already seen that HBrigone
adopted < as the sign for angle in 1634. Unfortunately, in 1631,
eHarriot's Artis analyticae praxis utilized this very symbol for "lew
than." Harriet's > and < for "greater than" and "less than" were
so well chosen, while the sign for "angle" could be easily modified so as
to remove the ambiguity, that the change of the symbol for angle was
eventually adopted. But c for angle persisted in its appearance,
especially during the seventeenth and eighteenth centuries. We find
it in W. Leybourn? J. Kersey? E. Hattoq6 E. Stone," J. Hodgson,7
D'Alembert's En~yclopkdie,~ Hall and Steven's Euclid,Q and Th.
Reye.lo John Caswellll used the sign to express "equiangular."
A popular modified sign for angle was L , in which the lower stroke
is horizontal and usually somewhat heavier. We have encountered
this in Oughtred's Trigonometria (1657), Caswell,12 Dulaurens,l3
1 G. S. Kliigel, Math. WOrterbuch, 1. Theil (Leipzig, 1803), art. "Bruchzeichen."
2 See, for instance, Euclid's Elements, Book V; see J. Gow, Histmy of Greek
Mathematics (1881), p. 106.
a William Leybourn, Panorganon: or a Universal Instrumenl (London, 1672),
p. 75. ,
'John Kersey, Algeba (London, 1673), Book IV, p. 177.
6 Edward Hatton, An Intire System of Arithmetic (London, 1721), p. 287.
8Edmund Stone, New Mathematid Didwnury (London, 1726; 2d ed., 1743),
art. "Character."
7 James Hodgson, A System of Mathematics, Vol. I (London, 1723), p. 10.
8 Encyclop6die ou Dictionnuire raissonnb, etc. (Diderot), Vol. VI (Lausanne et
Rerue, 1781), art. "Caractere."
Q H. S. Hall and F. H. Stevens. Euclid's Elements, Parts I and I1 (London,
1889), p. 10.
10 Theodor Reye, Die Geometric dm Lage (5th ed.; Leipzig, 1909), 1. Abteilung,
p.83. .
11 John Caswell, "Doctrine of Trigonometry," in Wallis' AEgeba (1685).
John Caswell, "Trigono.metry," in ibid.
la Francisci Dulaurens, Specimina mathemutica duobus libtie mprehensa
(Paris, 1667), "Symbols."