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

8 Spherical Geometry.
chord PD, describe the circle DEF. To describe a great circle,
it is necessary that the opening of the compass should be equal
to the chord of a quadrant. We can also, by the compass, divide
an angle into 2, 4, 8, &c., equal parts, erect an arc of a great
circle perpendicular to another, make a spherical angle equal
to a given spherical angle, describe a circle touching three given
circles, &c.
ExEnCISES.-I.
1. A great circle passing through the poles of two others cuts each at
right angles, and their points of intersection are its poles.
2-5. Solve the following problems with the compass:1~. Describe a great circle through two given points of the sphere.
2~. Through a given point of the sphere draw an arc of a great circle
perpendicular to a given great circle.
3~. Make, at a given point of a given great circle, an angle equal to
a given angle on the same sphere.
4~. Through a given point not on a given great circle draw a great
circle making a given angle with it.
6. The loci of the poles of great circles, making a given angle a with a
given great circle, consist of two small circles, having the same poles as the
given circle.
7. The tangents at a given point A of the sphere to all circles (great or
small) passing through A lie in the plane through A, perpendicular to the
radius of the sphere drawn to that point.
8. If a tangent line to a sphere passes through a given point, the locus of
the point of contact is a small circle.
9. If tangent lines to a sphere be parallel to a given line, the locus of the
points of contact is a great circle.
10. The arc of a great circle, perpendicular to the spherical radius of a
small circle at its extremity, touches the small circle.
11. Draw a great circle, touching two small circles.
12. Draw a great circle through a given point, touching a given small
circle.