A treatise on spherical trigonometry, and its application to geodesy and astronomy, with numerous examples. By John Casey.

CHAPTER IV.
VARIOUS APPLICATIONS.
SECTION I.-THEORY OF TRANSVERSALS.
69. DEF. XVIII.-Being given three points A, B, X on the
sin XA
same arc of a great circle, the ratio i X is called the ratio
sin XB
of section (AB, X).
The arcs XA, XB are considered of the same or of different
signs, according as they are measured in the same or in different directions from X. It is seen that it makes no difference
whether we take for XB the arc - XMIB or + XAX*'B, these
arcs having the same sign.
Br r
B= X
Fig. 22.
If A', B', X' be the antipodes of A, B, X, the ratio of section
(AB, X) is positive if X be on BA' or AB',
negative if X be on AB or 'B',
null,, at A or A',
infinite,, at B or B'.
F2