3. When the given circle is a right one, and the given point out of the centre.

Let X be the

given point in the

given right circle

C

AB.

Then draw A

XB, with the perpendicular di

ameter CD. Connect the points D and X. Bisect DX in E; and from E draw EF

at right angles to

A

X

B

F

D

DX. With the centre F project the circle CXD, which will be the circle required.

4. When the given circle is an oblique circle, and the given point in the middle of it.

Let X be the given point in CXD.

Through X and the centre draw the diameter AXB, and it will be the circle required.

5. When the given circle is an oblique one, and the given point out of the middle of it.

Let Y be the given point in CXD.

Find the poles P, p of the given oblique circle, and through P, Y, P draw the circle required.

C

B

P

D

A

PROBLEM

PROBLEM VI.

To set any number of degrees on a projected great circle.

3. On a given right circle from a point out of the centre.

4. From a given point on an oblique circle.

PROBLEM VII.

To measure any arc of a projected great circle.

PROBLEM VIII.

To measure any spherical angle.*

1. When the angle is at the centre of the primitive.

A spherical angle is measured by the arc of a great circle, intercepted between the two sides, that form the angle, at the distance of 90° from the angular point. Or the measure of a spherical angle is equal to the arc of a great circle, whose pole is the angular point, and which passes through the two poles of those great circles, which form the given angle. Hence a rule on the angular point and the poles of the arcs, which form the angle, cuts off, on the primitive, the measure of the angle required.