BOOK IF.

SPHERICAL GEOMETRY.

I0 5

THEOREM IX.

Of all great circle spherical trianglesABC, DEF, having one angle BAGin the one, equal to one angle EDFin the other, and the sides opposed tothem equal, that will have the greatestbase A B, whereof the opposite angleA C B differs the least from a right an-gle.—(PI. 5. fig. 3. and 4.)

Let B G and E H be arches perpendicularto A C and D F, in which produced take H K-HE, G I = G B, and BM = EH; (P. IV.B- I.) also let CI and KF be drawn. (P. I.B. I.)

The angle ICG being equal B C G, (con-verse C. VI. T. XX. B. I.) and the latter ofthese greater than E F H or K F H, by hy-pothesis : Thence, is angle IC B greater thanK F E j and, consequently, BI is greater than

LE: (T.VIII. B.IV.) Whence, BG = ®i is

,T 2

K E

greater than EH = ——’ or its equal BM,

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