...other, each to each, the two triangles will be congruent or symmetrical, and hence equal (15). xxui. If two spherical triangles on the same sphere, or equal spheres, have two angles of the one equal to two angles of the other, each to each, and the included sides equtd, the...

...equal in either case in all its parts to DEF. Proposition 10. Theorem.—If two triangles, on the same or equal spheres, have two sides and the included angle of one respectively equal to the two sides and the included of another, they are equal in all their parts....

...symmetrical is henceforth devoted entirely to such. THEOREM V. 688. Two spherical triangles having two sides and the included angle of one equal respectively to two sides and the included angle of the other, are either congruent or symmetrical. (1) If the parts given equal are arranged in the...

...symmetrical is henceforth devoted entirely to such. THEOREM V. 688. Two spherical triangles having two sides and the included angle of one equal respectively to two sides and the included angle of the other, are either congruent or symmetrical. (1) If the parts given equal are arranged in the...

...of its sides. Proposition 9. Theorem.* 709. Two triangles on the same, or on equal spheres, having two sides and the included angle of one equal respectively to two sides and the included angle of the other, are either equal or equivalent. Hyp. Let ABC, DEF be two A s having the side AB = DE,...

...line joining the two points. QED PROPOSITION IX. THEOREM. 275. Two triangles on equal spheres, having two sides and the included angle of one equal respectively to two sides and the included angle of the other, are either equal or equivalent. Proof. By superposing one Sph. A upon the other, or upon...

...mutually equilateral, their polar triangles are mutually equiangular. PROPOSITION XVII. THEOREM. 629. If two spherical triangles on the same sphere, or equal...equal respectively to two sides and the included angle of the other, I. They are equal if the equal parts occur in the same order. II. They are symmetrical...

...equiangular. (The proof is left to the student ; compare § 627.) PROPOSITION XVII. THEOREM. 629. If two spherical triangles on the same sphere, or equal...one equal respectively to two sides and the included anjle of the other, I. They are equal if tlte equal parts occur in the same order. II. They are symmetrical...

...mutually equiangular. PROPOSITION XVII. THEOREM. 629. If two spherical triangles on the same sphere, Br equal spheres, have two sides and the included angle...equal respectively to two sides and the included angle of the other, I. They are equal if the equal parts occur in the same order. II. They are symmetrical...

...hypothesis that angle «>angle c. Therefore AB<BC. QED PROPOSITION XXII. THEOREM 70. If two triangles have two sides and the included angle of one, equal respectively to two sides and the included angle of the other, the triangles are equal. C' GIVEN — AB, AC, and a, of the triangle ABC respectively...