. Mathematics, compiled from the best authors and intended to be the text-book of the course of private lectures on these sciences in the University at Cambridge [microform]. Thusjet GACEbe the pri-mitive circle, ADEI a greatcircle described through D,its centre being B. HK isa right line drawn throughB perpendicular to a rightline CI, passing through D,B, and the centre of theprimitive circle. Then thecentres of all other great cir-cles, as FDG, passing through D, will fall in the line HK. 8. Equal arcs of any two great circles of the sphere will beintercepted between two other circles, drawn
. Mathematics, compiled from the best authors and intended to be the text-book of the course of private lectures on these sciences in the University at Cambridge [microform]. Thusjet GACEbe the pri-mitive circle, ADEI a greatcircle described through D,its centre being B. HK isa right line drawn throughB perpendicular to a rightline CI, passing through D,B, and the centre of theprimitive circle. Then thecentres of all other great cir-cles, as FDG, passing through D, will fall in the line HK. 8. Equal arcs of any two great circles of the sphere will beintercepted between two other circles, drawn on the spherethrough the remotest poles of those great circles. For, let PBE A be a sphere,on which AGB and CFD aretwo great circles, whose re-motest poles are E and P ;and through these poles letthe great circle PBEC andthe small circle PGE bedrawn, cutting the great cir-cles AGB and CFD in thepoints B, G,D, F. Then are the intercepted arcs BG andDF equal to one SPHERIC GEOMETRY. 379 3. When the angular point is in the plane of the primitive. Let O be the point, _A. and 58° the angle. Draw a right lineDOB through the giv-en point O and thecentre of the circle,and cross it at rightangles with AE. Re-duce O to F in theprimitive ; make EGequal to DF ; reduceG to H ; through A, H, E, project a circle. Set the giv-en angle from A to K, and by laying a rule on O, K, cutthe oblique circle at X. Draw through X the perpendic-ular diameters WXY, QL ; and project the circle LOD is the angle required.
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