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properties of the cones of the second degree, amongst which 

 the following deserve to be noticed : 



1. If two fixed tangent arcs be drawn to a spherical 

 conic, and any third tangent arc be drawn meeting them in 

 two points, the arcs passing through these two points and 

 through the pole of a cyclic arc will intercept on that cyclic 

 arc a portion of a constant length. 



2. If from two fixed points in a spherical conic, arcs be 

 drawn to any third point on the curve, and produced to meet 

 one of the director arcs, they will intercept between them on 

 that director arc a portion which will subtend a constant 

 angle at the corresponding focus. 



3. A spherical conic and one of its cyclic arcs being 

 given, if, round the pole of this cyclic arc, as vertex, a spheri- 

 cal angle of variable magnitude be made to turn, whose sides 

 intercept between them on the cyclic arc a portion of a con- 

 stant length, the arc joining the points in which the sides of 

 the moveable angle meet the given conic will envelope a 

 second spherical conic : the given cyclic arc will be a cyclic 

 arc of the new conic, and this arc will have the same pole 

 with relation to the two curves. 



4. A spherical conic and one of its foci being given, if 

 round that focus, as vertex, a constant spherical angle be 

 made to turn, and from the points in which its sides meet the 

 director arc corresponding to the given focus, two arcs be 

 drawn touching the given conic, their point of concourse will 

 generate a second spherical conic : the given focus will be a 

 focus of the new conic, and the corresponding director arc 

 will be the same in the two curves. 



5. If a variable spherical angle turn round a fixed point 

 on the surface of a sphere so as to intercept between its sides 

 a constant segment on a fixed arc, the arc joining the points 

 in which its sides meet two other fixed arcs will envelope a 

 spherical conic touching these two fixed arcs. 



6. If a constant spherical angle turn round a fixed point 



