124 THE CONSTRUCTION QF

COR. I. Hence to construct a spherical tri-angle RIO, of which all the angles arid cur-vature of the sides are given. Join one of thegiven angles IPO, and by the foregoing pro-position draw the arch V I O of given curva-ture, meeting the former arches in given an-gles at I and O and the thing is done,

PROBLEM V.

To make a great circle spherical squareABDC, equal to. a given great circlespherical polygon E F G H I.--~(Pi. 7. fig,

Z- 4')

CON. On the arch AD, describe the per-pendicular OB, (P. VII, B. I.) and drawB D, cutting OB, OD, each in an angleOBD = ODB = one-eighth of the sum of theinterior angles of the polygon EFGHI. (C. I.P. IV.)

Produce B O and O D, and make the tri-angles COD, C O A, A O B, each equalBOD, (P. I. B. III.) and the thing is done,

DEM, The angles O B D, ODB, OCD,O A C, &c. are all equal by construction,and, therefore, there sum, viz. eight times