BOOK III. SPHERICAL GEOMETRY. 75

COR. II. If from any point C, three equalarches can be drawn to the circumference, thatpoint is the pole or center of the circle.

COR. III. The chord of G F is greater thanthat of G E, and that of G E than that ofG D. Also the chord of G H is less than thaof G A, and that of G A than that of G B.

COR. IV. Hence, if arches of equal curva-ture (the greatest of which must not exceed asemicircle) be drawn through the points G, F,G, E, G, B ; the greatest will be that G Fpasting through F, the extremity of the diameterHGCF that is drawn through G, and thepole C of the circle A E B.

Also, those that are nearer G F, as G Ewill be greater than those, as GD, that arefurther off.

And hence also the arch pasting throughH B will he less than that passing throughA G, &c»

THEOREM II.

If from a point G on the sphere with-out a circle, several arches be drawn tocut it ; of those that pass to the concave

K 2