P. HISTORY OF ' AATHEMATICAL - School of Mathematics

TRIGONOMETRY
155
lettering is employed by Oughtred in the books which bear his name
is one of several arguments in support of the view that Oughtred is
the author of the "Appendix."
519. European Continent during 1622-32.-Meanwhile, some attention
to symbolism continued to be given on the Continent. The
Danish astronomer, C. S. Longomontanus,' in 1622 used the notation
"S.R." for sinus rectus (sine), "S.T." for sinus totus (i.e., sin 90 0
or radius), "T." and "Tang." for tangens (tangent), "Sec." for secans
(secant), "T. copl." for "cotangent," "Sec. Compl." for "cosecant."
In 1626 a work was published at the Hague by Albert Girard of
Lorraine with the title Tables de sinus, tangentes et sicanie« selon le
raid de 10000 parties, of which a translation into Dutch appeared at
rJ
~ldT
tan.
H
tan.
p
sec. tan. tan.
B H a V
FIG. 119.-Illustrating Girard's notation in trigonometry
the Hague in 1629. 2 Girard uses in his formulae for right-angled
spherical triangles H, P, B to represent the hypothenuse, perpendicular,
and base, respectively, A to represent the angle at the vertex subtended
by the base, V the angle at the base subtended by the perpendicular;
a small letter a denotes the complement of capital A,
i.e., a=90 0-A. By a single letter is meant its sine; if a tangent or
secant is intended, the abbreviation for the function is given. Thus
Girard writes the formula shown in Figure 119, which means in
modern notation
tan P=sin (90 0 - A ) tan H ,
tan V=sec H tan (90 0-A) .
When Girard uses brackets he means that the sine of the quantity
included shall be taken. Thus, remembering that b=90 0-B, etc.,
1 Christian Longomontanus, Astronomiae Danicae (Amsterdam, 1622), Pars
prior, p, 12 fl.
2 Our information is drawn from J. W. L. Glaisher, op. cit., Vol. XLVI (1915),
p, 170-72; M. Cantor, Vorlesungen uber Geschichte der MathemaUk, Vol. II (2d
ed.; Leipzig, 1913), p, 708, 709; Vol. III (2d ed., 19(1), p, 559; A. von Braunmiihl,
Vorlesungen uberGeschichte der Trigonometrie, Vol. I (Leipzig, 1\KX», p. 237.