P. HISTORY OF ' AATHEMATICAL - School of Mathematics

TRIGONOMETRY
153
As far as the formulae for right-angled [spherical] triangles are concerned,
this table applies as follows. The sine of the angle on the left
multiplied by the sine of the upper angle in the square compartment,
gives the sine of the second angle in that compartment. Thus
Torporley means to say that
sin 24°Xsin 2e27'= sin 8°33' .
Those who like such questions may find out the meaning of the other
parts of the table..... Torporley was an astrologer."
The evidence at our command does not indicate that English
mathematicians of the early part of the seventeenth
century had seen the trigonometric
work of Finck, Lansberge, and Romanus on
the Continent. Some English authors were
familiar with the very influential work of
FIG.117.-Markingthe
Pitiscus, but he did not use abbreviations
given and required parts
for the trigonometric lines. The earliest efforts of a triangle (1618)
in the way of improved notation made in
England occur in that brief but remarkable anonymous "Appendix"
in the 1618 edition of Edward Wright's translation of Napier's
Descriptio. We quote the following from this"Appendix" :
"THE CALCULATION OF A PLAINE OBLIQUE ANGLED TRIANGLE
"1. Either the foure ingredient parts are opposite two to two: as
sB+BC=sD+DC.
"2. Or the two sides being given with the angle comprehended
within them, either of the other two angles is sought.
The angle B is 37~ 42' .
The side BC is 39 .
& the side BD is 85 ."1
Parts of the triangle are marked in the manner previously noted.
The equation by which the unknown side DC is to be computed involves
the Law of Sines. It is clear that the four tenus are intended
to represent logarithmic numbers; that is, sB means really log sin B;
BC stands for log (Be), etc. If such were not the intention, the
two signs of addition + would have to be replaced each by the sign
1 See Quarterly Journal of Pure and Applied Mathematics, Vol. XLVI (1915),
p.150.