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THE CONSTRUCTION OF

(C. I. T. V. B. II.) to each of these add thetriangle AD B; then is the triangle ADE =ABC.

PROBLEM III.

With two given arches A, B, to makea spherical rectangle.—(PI. 6. fig. 2 .)

ANALYSIS. Suppose the thing done, and thatIDCE is the rectangle required, having thefides IE = D C = A, and ID-EC-B, pro-duce D C and IE until they meet in V and L.

Since D C is given, VD=LC=LE=IVare all given ; and because ID is given, allthe sides of the triangle I V D are given; andhence the following :

CON. With the given lines IV, VD, andI D, make the triangle IV D; (P. I. B. III.)

and on V I, V D, produced, lay off IE andD C respectively, each equal the arch A.Lastly, through E, C, draw the great circleE C, and the thing is done.

The demonstration is evident from the analysis.

PROBLEM IV.

To draw a circle VIO D on the