BOOK 1. SPHERICAL PROBLEMS. 1 27

I A, B V, given in magnitude and posi-tion.—(PI. 5. fig. 19.)

ANALYSIS. Suppose that O, (^, afe thecenters of the given circles I A, B V, re-spectively. From O to Q^draw the great circleO Qj (P. I. B. I.) and join 0, I; V,with great circles, and produce the arches OI,V till they meet in P, which (becausethese arches are both perpendicular to IV) willbe the pole of I V. (C. II. P. V. B. I.)

Again, since O I and V Qj as well as IP =:P V, are given, P Qj= P V i V Q^, and P O--PI i 10, are also given; and also the tri-angle O P is given. Hence the following

CON. Having formed the triangle O P(P. I. B. III.) about P, as a pole with the ra-dius PI, describe the circle IV, which willtouch the circles I A, B V, in I and V, thepoints required as is plain from the analysis.

PROBLEM IX.

In a given less circle A D B C, to ap-ply an arch A B, equal in length and.curvature, to a given arch R S, (whosechord is less than the chord of the dia-