BOOK II. SPHERICAL GEOMETRY. 65

Also, since O A = I Qj (by construction) thetriangles OVA, ()y I, are equal and similar:Whence O V = Qjr.

Again, since C O is perpendicular to theplane OAa; (C IV. T. I. B. I.) and Calso perpendicular to the plane IP i Qj theangles C O V, C CsV, are each right ones ;and the triangles C O V, C Qj, equal andsimilar : Hence, angle O C V = Qju v and

00 = 00^

Also, since the angles O V C, Qjr C, areequal, and V A, VI, both perpendicular toV v: And the angles OVA, I v CV, eachequal a right angle ; the sections A a, I i,are parallel ; also, since O V is perpendicularto a A, and vC^to il, the, angles O V C,C v CV, which the planes a A O, QJ i, formwith the plane aAIi, are equal, and theseplanes, of consequence, will be parallel; andthe circles a A O, i IP , are equal by con-struction.

THEOREM VI.

From the equal fides A B, A C, of agreat circle Isosceles triangle ABC, let

I