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

Preliminary Propositions and Definitions. 3
Cor. 3.-Two circles, whose planes are equally distant from
the centre, are equal.
DEF. V.-The two points P, P' in which the diameter perpendicular to the plane of the circle DEF meets the sphere are called
its POLES.
From this definition it follows-1~. That all circles whose
planes are parallel have the same poles. 2~. That the centre
of any circle, its poles, and the centre of the sphere, are collinear.
DEF. VI.-A circle of the sphere whose plane passes through the
centre is called a GREAT CIRCLE, and a circle whose plane does not
pass through the centre is called a sMALL CIRCLE. Thus, on the
earth, the meridians, the equator, the ecliptic, are great circles,
and the parallels of latitude are small circles.
3. The curve of intersection of two spheres is a circle.
A 0/ OJ D
Fig. 2.
DEIM.-Let any plane passing through the centres 0, O' of
both spheres eut them in the circles AEBF, CEDF. Join
EF, 00', and produce 00' to meet the circles in A, D.
Now 00' bisects EF perpendicularly in I, and it is evident
when the semicircles AEB, CED revolve round the line 00'
to describe the spheres, that the point E will describe a circle,
having tbIfor its centre.
B2